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ThePEG  2.1.5
ThePEG::SpinHalfLorentzRotation Class Reference

The SpinHalfLorentzRotation class is designed to offer the same features as the HepLorentzRotation class of CLHEP but for the spin- $\frac12$ Lorentz transformation. More...

#include <SpinHalfLorentzRotation.h>

Public Member Functions

bool isIdentity () const
 Returns true if the Identity matrix.
 
SpinHalfLorentzRotation inverse () const
 Return the inverse.
 
SpinHalfLorentzRotationinvert ()
 Inverts the SpinHalfLorentzRotation matrix.
 
std::ostream & print (std::ostream &os) const
 output operator
 
Constructors and destructor.
 SpinHalfLorentzRotation ()
 Default constructor. More...
 
 SpinHalfLorentzRotation (double bx, double by, double bz, double gamma=-1.)
 Constructor giving the components of a Lorentz boost. More...
 
 SpinHalfLorentzRotation (const Boost &b, double gamma=-1.)
 Constructor giving the vector for a Lorentz boost. More...
 
Set methods for speical cases of simple rotations and boosts
SpinHalfLorentzRotationsetBoost (double bx, double by, double bz, double gamma=-1.)
 Specify the components of a Lorentz Boost. More...
 
SpinHalfLorentzRotationsetBoost (const Boost &b, double gamma=-1.)
 Specify a Lorentz Boost as a vector. More...
 
SpinHalfLorentzRotationsetBoostX (double &boost)
 Specify a boost by the given factor along the x-axis. More...
 
SpinHalfLorentzRotationsetBoostY (double &boost)
 Specify a boost by the given factor along the y-axis. More...
 
SpinHalfLorentzRotationsetBoostZ (double &boost)
 Specify a boost by the given factor along the z-axis. More...
 
SpinHalfLorentzRotationsetRotate (double delta, const Axis &axis)
 Specify a rotation about a general axis by the angle given. More...
 
SpinHalfLorentzRotationsetRotateX (double &angle)
 Specify a rotation by the given angle about the x-axis. More...
 
SpinHalfLorentzRotationsetRotateY (double &angle)
 Specify a rotation by the given angle about the y-axis. More...
 
SpinHalfLorentzRotationsetRotateZ (double &angle)
 Specify a rotation by the given angle about the z-axis. More...
 
Access methods for the components
Complex s1s1 () const
 The $(1,1)$ component.
 
Complex s1s2 () const
 The $(1,2)$ component.
 
Complex s1s3 () const
 The $(1,3)$ component.
 
Complex s1s4 () const
 The $(1,4)$ component.
 
Complex s2s1 () const
 The $(1,1)$ component.
 
Complex s2s2 () const
 The $(1,1)$ component.
 
Complex s2s3 () const
 The $(1,1)$ component.
 
Complex s2s4 () const
 The $(1,1)$ component.
 
Complex s3s1 () const
 The $(1,1)$ component.
 
Complex s3s2 () const
 The $(1,1)$ component.
 
Complex s3s3 () const
 The $(1,1)$ component.
 
Complex s3s4 () const
 The $(1,1)$ component.
 
Complex s4s1 () const
 The $(1,1)$ component.
 
Complex s4s2 () const
 The $(1,1)$ component.
 
Complex s4s3 () const
 The $(1,1)$ component.
 
Complex s4s4 () const
 The $(1,1)$ component.
 
Complex operator() (unsigned int i, unsigned int j) const
 Fortran style subscript operator.
 
Transformation and product members
SpinHalfLorentzRotation operator* (const SpinHalfLorentzRotation &lt) const
 Product of two SpinHalfLorentzRotations (this) * lt - matrix multiplication. More...
 
SpinHalfLorentzRotationoperator*= (const SpinHalfLorentzRotation &)
 Multiply by and assign a*=b becomes a= a*b.
 
SpinHalfLorentzRotationtransform (const SpinHalfLorentzRotation &)
 Transform (similar to *= but a.transform(b) becomes a = b*a.
 
SpinHalfLorentzRotationrotateX (double delta)
 Rotation around the x-axis; equivalent to LT = RotationX(delta) * LT.
 
SpinHalfLorentzRotationrotateY (double delta)
 Rotation around the y-axis; equivalent to LT = RotationY(delta) * LT.
 
SpinHalfLorentzRotationrotateZ (double delta)
 Rotation around the z-axis; equivalent to LT = RotationZ(delta) * LT.
 
SpinHalfLorentzRotationrotate (double delta, const Axis &axis)
 Rotation around specified vector - LT = Rotation(delta,axis)*LT.
 
SpinHalfLorentzRotationboostX (double beta)
 Pure boost along the x-axis; equivalent to LT = BoostX(beta) * LT.
 
SpinHalfLorentzRotationboostY (double beta)
 Pure boost along the y-axis; equivalent to LT = BoostX(beta) * LT.
 
SpinHalfLorentzRotationboostZ (double beta)
 Pure boost along the z-axis; equivalent to LT = BoostX(beta) * LT.
 
SpinHalfLorentzRotationboost (double bx, double by, double bz, double gamma=-1.)
 General boost equivalent to LT = Boost(bx,by,bz) * LT. More...
 
SpinHalfLorentzRotationboost (const Boost &bv, double gamma=-1.)
 General boost equivalent to LT = Boost(bv) * LT. More...
 

Protected Member Functions

 SpinHalfLorentzRotation (Complex s1s1, Complex s1s2, Complex s1s3, Complex s1s4, Complex s2s1, Complex s2s2, Complex s2s3, Complex s2s4, Complex s3s1, Complex s3s2, Complex s3s3, Complex s3s4, Complex s4s1, Complex s4s2, Complex s4s3, Complex s4s4)
 Protected constructor giving all the members, no check it is a valid transformation.
 

Private Types

using MatrixT = array< array< Complex, 4 >, 4 >
 

Private Member Functions

 SpinHalfLorentzRotation (const MatrixT &m)
 

Private Attributes

MatrixT _mx
 The members of the transformation matrix.
 

Friends

SpinHalfLorentzRotation inverseOf (const SpinHalfLorentzRotation &lt)
 The external inverseOf needs to be a friend.
 

Detailed Description

The SpinHalfLorentzRotation class is designed to offer the same features as the HepLorentzRotation class of CLHEP but for the spin- $\frac12$ Lorentz transformation.

This is then combined into the general LorentzRotation class of ThePEG to provide the Lorentz transformation for any object as the transformations for higher spin objects can be built from the spin- $\frac12$ and spin-1 transformations.

The boost matrix is calculated using the default Dirac matrix representation. Any conversion to other Dirac matrix representations must be handled when the transformation is used.

Definition at line 31 of file SpinHalfLorentzRotation.h.

Constructor & Destructor Documentation

◆ SpinHalfLorentzRotation() [1/3]

ThePEG::SpinHalfLorentzRotation::SpinHalfLorentzRotation ( )

Default constructor.

Gives a unit matrix.

Referenced by operator()().

◆ SpinHalfLorentzRotation() [2/3]

ThePEG::SpinHalfLorentzRotation::SpinHalfLorentzRotation ( double  bx,
double  by,
double  bz,
double  gamma = -1. 
)

Constructor giving the components of a Lorentz boost.

Parameters
bxThe x-component of the boost
byThe y-component of the boost
bzThe z-component of the boost
gammaThe $\gamma$ factor (optional)

◆ SpinHalfLorentzRotation() [3/3]

ThePEG::SpinHalfLorentzRotation::SpinHalfLorentzRotation ( const Boost b,
double  gamma = -1. 
)

Constructor giving the vector for a Lorentz boost.

Parameters
bThe boost vector
gammaThe $\gamma$ factor (optional)

Member Function Documentation

◆ boost() [1/2]

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::boost ( double  bx,
double  by,
double  bz,
double  gamma = -1. 
)

General boost equivalent to LT = Boost(bx,by,bz) * LT.

Parameters
bxThe x-component of the boost
byThe y-component of the boost
bzThe z-component of the boost
gammaThe $\gamma$ factor (optional)

Referenced by ThePEG::LorentzRotation::boost(), invert(), and operator()().

◆ boost() [2/2]

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::boost ( const Boost bv,
double  gamma = -1. 
)

General boost equivalent to LT = Boost(bv) * LT.

Parameters
bvThe boost vector
gammaThe $\gamma$ factor (optional)

◆ operator*()

SpinHalfLorentzRotation ThePEG::SpinHalfLorentzRotation::operator* ( const SpinHalfLorentzRotation lt) const

Product of two SpinHalfLorentzRotations (this) * lt - matrix multiplication.

Parameters
ltThe SpinHalfLorentzRotation we are multiplying

Referenced by operator()().

◆ setBoost() [1/2]

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::setBoost ( double  bx,
double  by,
double  bz,
double  gamma = -1. 
)

Specify the components of a Lorentz Boost.

Parameters
bxThe x-component of the boost
byThe y-component of the boost
bzThe z-component of the boost
gammaThe $\gamma$ factor (optional)

Referenced by invert(), and ThePEG::LorentzRotation::setBoost().

◆ setBoost() [2/2]

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::setBoost ( const Boost b,
double  gamma = -1. 
)

Specify a Lorentz Boost as a vector.

Parameters
bThe boost vector
gammaThe $\gamma$ factor (optional)

◆ setBoostX()

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::setBoostX ( double &  boost)

Specify a boost by the given factor along the x-axis.

Parameters
boostThe Lorentz boost

Referenced by invert(), and ThePEG::LorentzRotation::setBoostX().

◆ setBoostY()

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::setBoostY ( double &  boost)

Specify a boost by the given factor along the y-axis.

Parameters
boostThe Lorentz boost

Referenced by invert(), and ThePEG::LorentzRotation::setBoostY().

◆ setBoostZ()

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::setBoostZ ( double &  boost)

Specify a boost by the given factor along the z-axis.

Parameters
boostThe Lorentz boost

Referenced by invert(), and ThePEG::LorentzRotation::setBoostZ().

◆ setRotate()

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::setRotate ( double  delta,
const Axis axis 
)

Specify a rotation about a general axis by the angle given.

Parameters
deltaThe angle
axisThe axis

Referenced by invert(), and ThePEG::LorentzRotation::setRotate().

◆ setRotateX()

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::setRotateX ( double &  angle)

Specify a rotation by the given angle about the x-axis.

Parameters
angleThe rotation angle

Referenced by invert(), and ThePEG::LorentzRotation::setRotateX().

◆ setRotateY()

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::setRotateY ( double &  angle)

Specify a rotation by the given angle about the y-axis.

Parameters
angleThe rotation angle

Referenced by invert().

◆ setRotateZ()

SpinHalfLorentzRotation& ThePEG::SpinHalfLorentzRotation::setRotateZ ( double &  angle)

Specify a rotation by the given angle about the z-axis.

Parameters
angleThe rotation angle

Referenced by invert(), ThePEG::LorentzRotation::setRotateY(), and ThePEG::LorentzRotation::setRotateZ().


The documentation for this class was generated from the following file: