. The position of the wire and its current are vectors, but the magnetic field is a pseudovector ...?id Eo3mcd 62DsC&pg RA1 PA343&dq pseudovector 22magnetic field 22&cd 1 v onepage&q pseudovector 20 ... and mathematics , a pseudovector or axial vector is a quantity that transforms like a vector geometry ... on reflection matches its mirror image. In three dimensions the pseudovector p is associated with the cross ... books?id CRIjIx2ac6AC&pg PA125&dq 22C is a pseudovector. Note that 22&cd 1 v onepage&q ... The vector p calculated this way is a pseudovector. One example is the normal to a plane geometry ... by the right hand rule , and is a pseudovector. This has consequences in computer graphics where ... induces an extra sign flip because of its pseudovector nature, so the mirror flip in the end leaves ... Each wheel of a car driving away from an observer has an angular momentum pseudovector pointing left. The same is true for the mirror image of the car. As another example, consider the pseudovector ..., corresponding to the extra minus sign in the reflection of a pseudovector. This reflects the fact ... of a vector and a pseudovector is not meaningful. However, the weak force , which governs beta decay ... to x R x . If the vector v is a polar vector, it will be transformed to v R v . If it is a pseudovector ... mathbf v math pseudovector where the symbols are as described above, and the rotation matrix R can ... So v sub 3 sub is also a pseudovector. Similarly one can show that the difference between two pseudovectors is a pseudovector, that the sum or difference of two polar vectors is a polar vector, that multiplying a polar vector by any real number yields another polar vector, and that multiplying a pseudovector by any real number yields another pseudovector. On the other hand, suppose v sub 1 sub is known to be a polar vector, v sub 2 sub is known to be a pseudovector, and v sub 3 sub is defined ... nor a pseudovector. For an improper rotation, v sub 3 sub does not in general even keep the same magnitude ... more details
Unreferenced stub auto yes date December 2009 In high energy physics , a pseudovector meson or axial vector meson is a meson with total angular momentum quantum number total spin 1 and even parity physics parity usually noted as J sup P sup 1 sup sup . Compare to a vector meson , which has a total angular momentum quantum number total spin 1 and odd parity physics parity . The known pseudovector, or axial vector, mesons fall into two different classes those with J sup PC sup 1 sup sup , and those with J sup PC sup 1 sup sup . The first group have no spin excitation, but do have L 1. The latter group have both S 1 and L 1, with L and S coupling to J 1. The difference between the two groups gives them slightly different masses from the spin orbit coupling rule. The h and b mesons are in the first group, and should have heavier masses according to the spin orbit mass splitting in practice, however, they do not appear to follow this rule in nature, as evidenced by the f and a mesons being heavier. There are considerable experimental uncertainties in pseudovector meson masses which will require additional experimental data to clarify. The 1 sup sup multiplet of light mesons may show similar behavior to that of the vector mesons, in that the mixing of light quarks with strange quarks appears to be small for this quantum number. The 1 sup sup multiplet, on the other hand, may be affected by other factors that cause generally reduced meson masses. Further experimentation is required in order to clarify the observed situation. Pseudovector, or axial vector, mesons in the 1 sup sup channel may most readily be seen in proton antiproton annihilation and pion nucleon scattering. The mesons in the 1 sup sup channel are normally seen in proton proton and pion nucleon scattering. Examples 1 sup sup candidates h sub 1 sub 1170 , b sub 1 sub 1235 , h sub 1 sub 1380 1 sup sup candidates ... 1 sub 1400 heavy candidates h sub c sub , chi sub c1 sub See also List of mesons DEFAULTSORT Pseudovector ... more details
Orphan date April 2010 The Pauli Lubanski pseudovector is an operator in quantum field theory defined as math W mu frac 1 2 epsilon mu nu rho sigma J nu rho P sigma math where math epsilon mu nu rho sigma math is the totally antisymmetric Levi Civita tensor math J nu rho math is the angular momentum operator math P sigma math is the four momentum math W mu math satisfies the following commutation relations, math P mu ,W nu 0 math math J mu nu ,W rho i g rho nu W mu g rho mu W nu math Moreover, it satisfies math P mu W mu 0 math In quantum field theory, in the case of a massive field, the Casimir invariant math W mu W mu math describes the total spin of the particle, and has the eigenvalues math W 2 W mu W mu m 2 s s 1 math where s is the spin of the particle. It is very easy to see this if you go to the rest frame of the particle where math vec W m vec J math and math W 0 0 math , so math W mu W mu m 2 vec J . vec J math . Since this is a Lorentz invariant quantity it will be the same in all the other frames. It is also customary to take math W 3 math to describe the spin projection along the third direction in the rest frame. In the case of a non massive field, math W 0 vec J . vec P math is the Helicity particle physics helicity operator. Category Quantum field theory ko ... more details
object to describe a physical quantity. In 3 space, quantities which are described by a pseudovector are in fact skew symmetric tensors of rank 3, which are invariant under inversion. The pseudovector ... and skew symmetric tensors of rank 2. The dual of a pseudovector is a skew symmetric tensors of rank 2 and vice versa . It is the tensor and not the pseudovector which is the representation of the physical quantity which is invariant to a coordinate inversion, while the pseudovector is not invariant ... a vector the surface normal and pseudovector the magnetic field , the Helicity particle physics helicity is the projection dot product of a spin physics spin pseudovector onto the direction of momentum ... more details
Unreferenced date June 2007 In high energy physics , a vector meson is a meson with total angular momentum quantum number total spin 1 and odd parity physics parity usually noted as nowrap J sup P sup 1 sup &minus sup . Compare to a pseudovector meson , which has a total angular momentum quantum number total spin 1 and even parity physics parity . Vector mesons have been seen in experiments since the 1960s, and are well known for their spectroscopic pattern of masses. Since the development of the quark model by Murray Gell Mann and independently by George Zweig as well , the vector mesons have demonstrated the spectroscopy of pure states. The fact that the nowrap Isospin I 1 rho meson &rho and nowrap I 0 omega meson &omega have nearly equal mass centered around 770 val 780 ul MeV c2 , while the phi meson &phi has a higher mass around val 1020 u MeV c2 , indicates that the light quark vector mesons appear in nearly pure states with the &phi meson having a nearly 100 percent amplitude of hidden strangeness . This characteristic of the vector mesons is not at all evident in the pseudoscalar meson or scalar meson multiplets, and may be only slightly realized among the tensor meson and pseudovector meson multiplets. This fact makes the vector mesons an excellent probe of the quark flavour physics flavor content of other types of mesons, measured through the respective decay rate s of non vector mesons into the different types of vector mesons. Such experiments are very revealing for theorists who seek to determine the flavor content of mixed state mesons. At higher masses, the vector mesons include charm quark charm and bottom quark s in their structure. In this realm, the radiative process es tend to stand out, with heavy tensor and scalar mesons decaying dominantly into vector mesons by photon emission . Pseudovector mesons transition by a similar process into pseudoscalar mesons. Because much of the spectrum of heavy mesons is tied by radiative processes to the vector ... more details
product transforms as a pseudovector under parity transformations and so is properly described as a pseudovector. The dot product of two vectors is a scalar but the dot product of a pseudovector ... Elsevier Publishing Company, Inc pages 262 263 year 1970 ref Vector or pseudovector Where parity transformation s need to be considered, so the cross product is treated as a pseudovector , the vector triple product is vector rather than pseudovector valued, as it is the product of a vector a and a pseudovector ... more details
Refimprove date December 2009 In particle physics , a vector boson is a boson with the spin physics spin quantum number equal to 1. The vector bosons considered to be elementary particle s in the Standard Model are the gauge boson s or, the force carrier s of fundamental interaction s the photon of electromagnetism , the W and Z bosons of the weak interaction , and the gluon of the strong interaction . There also exist composite particle s that are vector bosons, such as the vector meson s, made of a quark and antiquark . For some time, through the 1970s and 80s, intermediate vector bosons , vector bosons of intermediate mass, were a major topic in high energy physics . Citation needed date January 2009 Explanation The name vector boson arises from quantum field theory . The vector component component of such a particle s spin along any axis has the three eigenvalue s , 0, and where is the reduced Planck constant , meaning that any measurement of it can only yield one of these values. This is, at least, true for massive vector bosons the situation is a bit different for massless particles such as the photon, for reasons beyond the scope of this article. ref Weingard, Robert. http bjps.oxfordjournals.org content 40 2 287.full.pdf Some Comments Regarding Spin and Relativity ref The space of spin states therefore has three Degrees of freedom physics and chemistry degrees of freedom Citation needed date September 2011 , the same as the number of components of a vector physics vector in three dimensional space. Quantum superposition s of these states can be taken such that they transform under rotation s just like the spatial components of a rotating vector Citation needed date September 2011 . If the vector boson is taken to be the quantum of a field, the field is a vector field , hence the name. Notes Reflist See also Pseudovector meson Scalar boson DEFAULTSORT Vector Boson Category Bosons Category Mesons Category Quantum field theory Particle stub es Bos n vecto ... more details
angle multiplying a unit vector along some rotation axis here assumed fixed as its pseudovector or axial ... surroundings is identified with a unit quaternion having a zero pseudovector part and 1 for the scalar part, then after one complete rotation 2pi rad the pseudovector part returns to zero and the scalar part has become 1 entangled . After two complete rotations 4pi rad the pseudovector part again ... more details
Orphan date November 2006 In Newtonian mechanics , many of the quantities in linear motion and rotational motion are analogous, in that they act the same way in many equations. Note that the vector quantities in rotational motion are actually pseudovector s which point along the axis of rotation according to the right hand rule . border colspan 2 Linear quantities colspan 2 Rotational quantities math vec s math displacement vector displacement math vec theta math angular displacement ref In some ways, angular displacement should not be considered a vector, because addition of angular displacements unlike vectors is not commutative, since rotation is not commutative in 3 or more dimensions. ref math vec v math velocity math vec omega math angular velocity math vec a math acceleration math vec alpha math angular acceleration math m math mass math I math moment of inertia math vec p math momentum math vec L math angular momentum math vec F math force math vec tau math torque border Linear motion Rotational motion math vec v frac d vec s dt math math vec omega frac d vec theta dt math math vec a frac d vec v dt math math vec alpha frac d vec omega dt math math vec p m vec v math math vec L I vec omega math math vec F m vec a math math vec tau I vec alpha math math vec F frac d vec p dt math math vec tau frac d vec L dt math math dW vec F cdot d vec s math math dW vec tau cdot d vec theta math math E frac1 2 mv 2 math math E frac1 2 I omega 2 math Footnotes div class references small references div br Category Classical mechanics Category Fundamental physics concepts ... more details
occurs. The direction of the angular velocity pseudovector will be along the axis of rotation in this case ... in this case is generally thought of as a vector, or more precisely, a pseudovector . It now has not only ... velocity pseudovector. Being math vec u math an unitary vector over the instantaneous rotation axis ... velocity pseudovector, while the magnitude is the same as the pseudoscalar value found in the 2 dimensional ... defined like this, angular velocity, which is a pseudovector, becomes also a real vector because ... thumb Diagram showing Euler frame in green The components of the angular velocity pseudovector ... frame the intrinsic rotation axis Euler proved that the projections of the angular velocity pseudovector ... 1 and 2. ref Exponential of W In three dimensions angular velocity can be represented by a pseudovector ... velocity pseudovector math omega math is the following. Because of W is the derivative of an orthogonal ... velocity pseudovector parallel to it, and would only allow the computation of the component ... space dual to get a 3 dimensional pseudovector which is precisely the previous angular velocity vector ... more details
, the curl of a vector field is a pseudovector field, and if one reflects a vector field, the curl points ... scalar fields are 0 vector fields, vector fields are 1 vector fields, pseudovector fields are 2 vector ... types of fields scalar vector pseudovector pseudoscalar corresponding to 0 1 n &minus 1 n dimensions ... form hence pseudovector field , which is then interpreted as a vector field, rather than directly taking ... more details
The principle of Microscopic reversibility in physics and chemistry is twofold First, it states that the microscopic detailed dynamics of particles and fields is time reversible because the microscopic equations of motion are symmetric with respect to inversion in time T symmetry Second, it relates to the statistical description of the kinetics of macroscopic or mesoscopic systems as an ensemble of elementary processes collisions, elementary transitions or reactions. For these processes, the consequence of the microscopic T symmetry is blockquote Corresponding to every individual process there is a reverse process, and in a state of equilibrium the average rate of every process is equal to the average rate of its reverse process. ref Lewis, G.N. 1925 http www.pnas.org content 11 3 179.full.pdf html A new principle of equilibrium , PNAS March 1, 1925 vol. 11 no. 3 179 183. ref blockquote Time reversibility of dynamics The Newton s laws of motion Newton and the Schr dinger equation s in the absence of the macroscopic magnetic field s and in the inertial frame of reference are T invariant if X t is a solution then X t is also a solution here X is the vector of all dynamic variables, including all the coordinates of particles for the Newton equations and the wave function in the configuration space for the Schr dinger equation . There are two sources of the violation of this rule First, if dynamics depend of a pseudovector like the magnetic field or the rotation angular speed in the rotating frame then the T symmetry does not hold. Second, in microphysics of weak interaction the T symmetry may be violated and only the combined CPT symmetry holds. Macroscopic consequences of the time reversibility of dynamics In physics and chemistry, there are two main macroscopic consequences of the time reversibility of microscopic dynamics the principle of detailed balance and the Onsager reciprocal relations . The statistical description of the macroscopic process as an ensemble of ... more details
in various ways it can be made independent of orientation by changing the result to pseudovector , or in arbitrary ... is not a true vector, but rather a pseudovector . See Cross product Cross product and handedness cross ... of the coordinate system is not fixed a priori, the result is not a true vector but a pseudovector . Therefore, for consistency, the other side must also be a pseudovector. Citation needed date April 2008 More generally, the result of a cross product may be either a vector or a pseudovector, depending ... in the following ways under application of the cross product vector × vector pseudovectorpseudovector × pseudovectorpseudovector vector × pseudovector vector pseudovector ... and the other one is a pseudovector e.g. , the cross product of two vectors . For instance, a vector ... than three vectors Cartesian product A product of two sets the symbol Bivector Pseudovector Notes ... more details
Dablink See scalar disambiguation scalar for an account of the broader concept also used in mathematics and computer science. In physics , a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations in Newtonian mechanics , or by Lorentz transformation s or space time translations in relativity . This is in contrast to a vector physics vector . A related concept is a pseudoscalar physics pseudoscalar , which is invariant under proper rotation s but like a pseudovector flips sign under improper rotation s. Physical quantity Main Physical quantity A physical quantity is expressed as the product mathematics product of a number numerical value and a physical unit , not merely a number. The quantity does not depend on the unit i.e for distance, 1 km is the same as 1000 m , although the number depends on the unit. Thus, following the example of distance, the quantity does not depend on the length of the base vectors of the coordinate system. Also, other changes of the coordinate system may affect the formula for computing the scalar for example, the Euclidean formula for distance in terms of coordinates relies on the basis being orthonormal , but not the scalar itself. In this sense, physical distance deviates from the definition of Metric mathematics metric in not being just a real number however it satisfies all other properties. The same applies for other physical quantities which are not dimensionless. Examples Some examples of scalars include the mass , charge physics charge , or the temperature , ref harvnb Feynman Leighton Sands 1963 ref or electric potential at a point inside a medium. The distance between two points in three dimensional space is a scalar, but the Direction geometry, geography direction from one of those points to the other is not, since describing a direction requires two physical quantities such as the angle on the horizontal plane and the angle away from that plane. Force cannot be described using a ... more details
See also Exterior algebra Bivector Geometric product In geometric algebra , a blade is a generalization of the notion of Euclidean vector vector s and Scalar mathematics scalars to include bivector s, trivector s, etc. In detail ref name Rodrigues cite book title Invariants for pattern recognition and classification author Marcos A. Rodrigues chapter 1.2 Geometric algebra an outline url http books.google.com books?id QbFSt0SlDjIC&pg PA3 page 3 ff isbn 9810242786 year 2000 publisher World Scientific ref A scalar or 0 blade of grade 0 is the inner product or dot product of two vectors a and b denoted as math boldsymbol a cdot b . math A vector is a 1 blade of grade 1. A 2 blade of grade 2 is a simple bivector sums of 2 blades also are bivectors, but may not be simple , given by the wedge product of two vectors a and b math boldsymbol a wedge b . math A 3 blade of grade 3 is a trivector , that is, a wedge product of three vectors, a , b and c math boldsymbol a wedge b boldsymbol wedge c . math A k blade is a blade of graded algebra grade k . The highest grade element in a space is called the pseudoscalar . ref name Vince cite book url http books.google.com books?id 3VxZqfm3I MC&pg PA85&dq pseudoscalar 22highest grade 22&lr &as drrb is q&as minm is 0&as miny is &as maxm is 0&as maxy is &as brr 0&cd 1 v onepage&q pseudoscalar 20 22highest 20grade 22&f false title Geometric algebra for computer graphics author John A. Vince page 85 isbn 1846289963 year 2008 publisher Springer ref In a space of dimension n , the blade of grade n 1 is called a pseudovector . ref name Baylis01 cite book url http books.google.com books?id oaoLbMS3ErwC&pg PA100&dq 22pseudovectors 28grade n 1 elements 29 22&lr &as drrb is q&as minm is 0&as miny is &as maxm is 0&as maxy is &as brr 0&cd 1 v onepage&q 22pseudovectors 20 28grade 20n 20 201 20elements 29 22&f false page 100 author William E Baylis title Lectures on Clifford geometric algebras and applications isbn 0817632573 year 2004 chapter 4.2.3 ... more details
as that of momentum per unit charge. Although the magnetic field B is a pseudovector ... is a pseudovector, and vice versa. ref name Fitzpatrick Gauge choices main Gauge fixing The above definition ... more details
1 sup style text align center T sup 1 sup scalar or pseudovector Angular momentum style text align center ... s sup 1 sup style text align center M L sup 2 sup T sup 1 sup conserved quantity, pseudovector Area ... text align center M T sup 2 sup I sup 1 sup pseudovector field Magnetization style text align center ... text align center M L sup 2 sup T sup 2 sup pseudovector Velocity style text align center v Speed ... more details
In mathematical physics , spacetime algebra STA is a name for the Clifford algebra C & x2113 sub 1,3 sub R ,or Geometric algebra G sub 4 sub G Minkowski Space M4 which can be particularly closely associated with the geometry of special relativity and relativistic spacetime . It is a linear algebra allowing not just Vector geometric vector s, but also bivector directed quantities associated with particular planes for example areas, or rotations or multivector associated with particular hyper volume s to be combined, as well as rotation rotated , Reflection mathematics reflected , or Lorentz boost ed. It is also the natural parent algebra of spinor s in special relativity. These properties allow many of the most important equations in physics to be expressed in particularly simple forms and can be very helpful towards a more geometrical understanding of their meanings. Structure The spacetime algebra is built up from combinations of one time like basis vector math gamma 0 math and three orthogonal space like vectors, math gamma 1, gamma 2, gamma 3 math , under the multiplication rule math displaystyle gamma mu gamma nu gamma nu gamma mu 2 eta mu nu math where math eta mu nu , math is the Minkowski metric with signature &minus &minus &minus Thus math gamma 0 2 1 math , math gamma 1 2 gamma 2 2 gamma 3 2 1 math , otherwise math displaystyle gamma mu gamma nu gamma nu gamma mu math . The basis vectors math gamma k math share the same properties as the Dirac matrix Dirac matrices , but no explicit matrix representation is utilized in STA. This generates a basis of one Scalar mathematics scalar , math 1 math , four Vector geometric vector s math gamma 0, gamma 1, gamma 2, gamma 3 math , six bivector s math gamma 0 gamma 1, , gamma 0 gamma 2, , gamma 0 gamma 3, , gamma 1 gamma 2, , gamma 2 gamma 3, , gamma 3 gamma 1 math , four pseudovector s math i gamma 0, i gamma 1, i gamma 2, i gamma 3 math and one pseudoscalar math i gamma 0 gamma 1 gamma 2 gamma 3 math . Reciprocal fr ... more details
quantities and transform in a similar way under changes of the coordinate system include pseudovector ... for left handed as well as right handed coordinate systems the cross product of two vectors is a pseudovector .... A vector which gains a minus sign when the orientation of space changes is called a pseudovector or an axial ... vectors. One example of a pseudovector is angular velocity . Driving in a car , and looking forward ... of relativity relativity Normal vector Null vector Pseudovector Tangential and normal components ... more details
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