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.

SpinHalfLorentzRotation &	invert ()
	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
SpinHalfLorentzRotation &	setBoost (double bx, double by, double bz, double gamma=-1.)
	Specify the components of a Lorentz Boost. More...

SpinHalfLorentzRotation &	setBoost (const Boost &b, double gamma=-1.)
	Specify a Lorentz Boost as a vector. More...

SpinHalfLorentzRotation &	setBoostX (double &boost)
	Specify a boost by the given factor along the x-axis. More...

SpinHalfLorentzRotation &	setBoostY (double &boost)
	Specify a boost by the given factor along the y-axis. More...

SpinHalfLorentzRotation &	setBoostZ (double &boost)
	Specify a boost by the given factor along the z-axis. More...

SpinHalfLorentzRotation &	setRotate (double delta, const Axis &axis)
	Specify a rotation about a general axis by the angle given. More...

SpinHalfLorentzRotation &	setRotateX (double &angle)
	Specify a rotation by the given angle about the x-axis. More...

SpinHalfLorentzRotation &	setRotateY (double &angle)
	Specify a rotation by the given angle about the y-axis. More...

SpinHalfLorentzRotation &	setRotateZ (double &angle)
	Specify a rotation by the given angle about the z-axis. More...

Access methods for the components
Complex	s1s1 () const
	The component.

Complex	s1s2 () const
	The component.

Complex	s1s3 () const
	The component.

Complex	s1s4 () const
	The component.

Complex	s2s1 () const
	The component.

Complex	s2s2 () const
	The component.

Complex	s2s3 () const
	The component.

Complex	s2s4 () const
	The component.

Complex	s3s1 () const
	The component.

Complex	s3s2 () const
	The component.

Complex	s3s3 () const
	The component.

Complex	s3s4 () const
	The component.

Complex	s4s1 () const
	The component.

Complex	s4s2 () const
	The component.

Complex	s4s3 () const
	The component.

Complex	s4s4 () const
	The 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...

SpinHalfLorentzRotation &	operator*= (const SpinHalfLorentzRotation &)
	Multiply by and assign a=b becomes a= ab.

SpinHalfLorentzRotation &	transform (const SpinHalfLorentzRotation &)
	Transform (similar to = but a.transform(b) becomes a = ba.

SpinHalfLorentzRotation &	rotateX (double delta)
	Rotation around the x-axis; equivalent to LT = RotationX(delta) * LT.

SpinHalfLorentzRotation &	rotateY (double delta)
	Rotation around the y-axis; equivalent to LT = RotationY(delta) * LT.

SpinHalfLorentzRotation &	rotateZ (double delta)
	Rotation around the z-axis; equivalent to LT = RotationZ(delta) * LT.

SpinHalfLorentzRotation &	rotate (double delta, const Axis &axis)
	Rotation around specified vector - LT = Rotation(delta,axis)*LT.

SpinHalfLorentzRotation &	boostX (double beta)
	Pure boost along the x-axis; equivalent to LT = BoostX(beta) * LT.

SpinHalfLorentzRotation &	boostY (double beta)
	Pure boost along the y-axis; equivalent to LT = BoostX(beta) * LT.

SpinHalfLorentzRotation &	boostZ (double beta)
	Pure boost along the z-axis; equivalent to LT = BoostX(beta) * LT.

SpinHalfLorentzRotation &	boost (double bx, double by, double bz, double gamma=-1.)
	General boost equivalent to LT = Boost(bx,by,bz) * LT. More...

SpinHalfLorentzRotation &	boost (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

bx	The x-component of the boost
by	The y-component of the boost
bz	The z-component of the boost
gamma	The $\gamma$ factor (optional)

◆ SpinHalfLorentzRotation() [3/3]

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

Constructor giving the vector for a Lorentz boost.

Parameters

b	The boost vector
gamma	The $\gamma$ 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

bx	The x-component of the boost
by	The y-component of the boost
bz	The z-component of the boost
gamma	The $\gamma$ 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

bv	The boost vector
gamma	The $\gamma$ factor (optional)

◆ operator*()

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

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

Parameters

lt	The 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

bx	The x-component of the boost
by	The y-component of the boost
bz	The z-component of the boost
gamma	The $\gamma$ 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

b	The boost vector
gamma	The $\gamma$ factor (optional)

◆ setBoostX()

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

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

Parameters

boost The 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

boost The 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

boost The 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

delta	The angle
axis	The 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

angle The 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

angle The rotation angle

Referenced by invert().

◆ setRotateZ()

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

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

Parameters

angle The rotation angle

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

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

SpinHalfLorentzRotation.h

Public Member Functions

Protected Member Functions

Private Types

Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ SpinHalfLorentzRotation() [1/3]

◆ SpinHalfLorentzRotation() [2/3]

◆ SpinHalfLorentzRotation() [3/3]

Member Function Documentation

◆ boost() [1/2]

◆ boost() [2/2]

◆ operator*()

◆ setBoost() [1/2]

◆ setBoost() [2/2]

◆ setBoostX()

◆ setBoostY()

◆ setBoostZ()

◆ setRotate()

◆ setRotateX()

◆ setRotateY()

◆ setRotateZ()