The LorentzTensor class is designed to implement the storage of a complex tensor to be used to representation the wavefunction of a spin-2 particle. More...

#include <LorentzTensor.h>

Inheritance diagram for ThePEG::Helicity::LorentzTensor< Value >:

[legend]

Public Member Functions
Standard constructors and destructors.
	LorentzTensor ()=default
	Default zero constructor.

	LorentzTensor (complex< Value > xx, complex< Value > xy, complex< Value > xz, complex< Value > xt, complex< Value > yx, complex< Value > yy, complex< Value > yz, complex< Value > yt, complex< Value > zx, complex< Value > zy, complex< Value > zz, complex< Value > zt, complex< Value > tx, complex< Value > ty, complex< Value > tz, complex< Value > tt)
	Constructor specifyign all components.

	LorentzTensor (const LorentzPolarizationVector &p, const LorentzPolarizationVector &q)
	Constructor in terms of two polarization vectors.

Access individual components.
complex< Value >	xx () const
	Get x,x component.

complex< Value >	yx () const
	Get y,x component.

complex< Value >	zx () const
	Get z,x component.

complex< Value >	tx () const
	Get t,x component.

complex< Value >	xy () const
	Get x,y component.

complex< Value >	yy () const
	Get y,y component.

complex< Value >	zy () const
	Get z,y component.

complex< Value >	ty () const
	Get t,y component.

complex< Value >	xz () const
	Get x,z component.

complex< Value >	yz () const
	Get y,z component.

complex< Value >	zz () const
	Get z,z component.

complex< Value >	tz () const
	Get t,z component.

complex< Value >	xt () const
	Get x,t component.

complex< Value >	yt () const
	Get y,t component.

complex< Value >	zt () const
	Get z,t component.

complex< Value >	tt () const
	Get t,t component.

void	setXX (complex< Value > a)
	Set x,x component.

void	setYX (complex< Value > a)
	Set y,x component.

void	setZX (complex< Value > a)
	Set z,x component.

void	setTX (complex< Value > a)
	Set t,x component.

void	setXY (complex< Value > a)
	Set x,y component.

void	setYY (complex< Value > a)
	Set y,y component.

void	setZY (complex< Value > a)
	Set z,y component.

void	setTY (complex< Value > a)
	Set t,y component.

void	setXZ (complex< Value > a)
	Set x,z component.

void	setYZ (complex< Value > a)
	Set y,z component.

void	setZZ (complex< Value > a)
	Set z,z component.

void	setTZ (complex< Value > a)
	Set t,z component.

void	setXT (complex< Value > a)
	Set x,t component.

void	setYT (complex< Value > a)
	Set y,t component.

void	setZT (complex< Value > a)
	Set z,t component.

void	setTT (complex< Value > a)
	Set t,t component.

complex< Value >	operator() (int i, int j) const
	Get components by indices.

complex< Value > &	operator() (int i, int j)
	Set components by indices.

Transformations.
LorentzTensor &	boost (double, double, double)
	Standard Lorentz boost specifying the components of the beta vector.

LorentzTensor< Value > &	boost (const Boost &b)
	Standard Lorentz boost specifying the beta vector.

LorentzTensor &	transform (const SpinOneLorentzRotation &r)
	General Lorentz transformation.

LorentzTensor< Value >	conjugate ()
	Return the complex conjugate.

Arithmetic operators.
std::array< std::array< complex< Value >, 4 >, 4 >	_tensor
	The components.

LorentzTensor< Value >	operator*= (Complex a)
	Scaling with a complex number.

LorentzTensor< Value >	operator+ (const LorentzTensor< Value > &in) const
	Addition.

LorentzTensor< Value >	operator- (const LorentzTensor< Value > &in) const
	Subtraction.

complex< Value >	trace () const
	Trace.

template<typename ValueB >
auto	innerProduct (const LorentzTensor< ValueB > &ten) const -> LorentzTensor< decltype(ten.xx().real() *this->xx().real())>
	Inner product with another tensor.

template<typename ValueB >
auto	outerProduct (const LorentzTensor< ValueB > &ten) const -> LorentzTensor< decltype(ten.xx().real() *this->xx().real())>
	Outer product with another tensor.

template<typename ValueB >
auto	preDot (const LorentzVector< complex< ValueB > > &vec) const -> LorentzVector< decltype(vec.x() *this->xx())>
	Various dot products.

template<typename ValueB >
auto	postDot (const LorentzVector< complex< ValueB > > &vec) const -> LorentzVector< decltype(vec.x() *this->xx())>
	Second index dot product with polarization vector.

auto	preDot (const Lorentz5Momentum &vec) const -> LorentzVector< decltype(vec.x() *this->xx())>
	First index dot product with momentum.

auto	postDot (const Lorentz5Momentum &vec) const -> LorentzVector< decltype(vec.x() *this->xx())>
	Second index dot product with momentum.

template<typename T , typename U >
auto	operator* (const LorentzTensor< T > &t, const LorentzTensor< U > &u) -> decltype(t.xx() *u.xx())
	Scalar product with other tensor.

Detailed Description

template<typename Value>
class ThePEG::Helicity::LorentzTensor< Value >

The LorentzTensor class is designed to implement the storage of a complex tensor to be used to representation the wavefunction of a spin-2 particle.

At the moment it only implements the storage of the tensor components but it is envisaged that it will be extended to include boost methods etc.

Author: Peter Richardson

Definition at line 37 of file LorentzTensor.h.

Constructor & Destructor Documentation

◆ LorentzTensor() [1/2]

template<typename Value >

ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor	(	complex< Value >	xx,
		complex< Value >	xy,
		complex< Value >	xz,
		complex< Value >	xt,
		complex< Value >	yx,
		complex< Value >	yy,
		complex< Value >	yz,
		complex< Value >	yt,
		complex< Value >	zx,
		complex< Value >	zy,
		complex< Value >	zz,
		complex< Value >	zt,
		complex< Value >	tx,
		complex< Value >	ty,
		complex< Value >	tz,
		complex< Value >	tt
	)

inline

Constructor specifyign all components.

Definition at line 51 of file LorentzTensor.h.

◆ LorentzTensor() [2/2]

template<typename Value >

ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor	(	const LorentzPolarizationVector &	p,
		const LorentzPolarizationVector &	q
	)

inline

Constructor in terms of two polarization vectors.

Definition at line 66 of file LorentzTensor.h.

Member Function Documentation

◆ boost()

template<typename Value >

LorentzTensor< Value > & ThePEG::Helicity::LorentzTensor< Value >::boost ( const Boost & b )

inline

Standard Lorentz boost specifying the beta vector.

Definition at line 267 of file LorentzTensor.h.

◆ conjugate()

template<typename Value >

LorentzTensor< Value > ThePEG::Helicity::LorentzTensor< Value >::conjugate ( )

inline

Return the complex conjugate.

Definition at line 295 of file LorentzTensor.h.

◆ innerProduct()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzTensor< Value >::innerProduct ( const LorentzTensor< ValueB > & ten ) const -> LorentzTensor<decltype(ten.xx().real()*this->xx().real())>

inline

Inner product with another tensor.

Definition at line 355 of file LorentzTensor.h.

◆ operator()() [1/2]

template<typename Value >

complex< Value > & ThePEG::Helicity::LorentzTensor< Value >::operator()	(	int	i,
		int	j
	)

inline

Set components by indices.

Definition at line 251 of file LorentzTensor.h.

◆ operator()() [2/2]

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::operator()	(	int	i,
		int	j
	)		const

inline

Get components by indices.

Definition at line 243 of file LorentzTensor.h.

◆ operator*=()

template<typename Value >

LorentzTensor< Value > ThePEG::Helicity::LorentzTensor< Value >::operator*= ( Complex a )

inline

Scaling with a complex number.

Definition at line 309 of file LorentzTensor.h.

◆ operator+()

template<typename Value >

LorentzTensor< Value > ThePEG::Helicity::LorentzTensor< Value >::operator+ ( const LorentzTensor< Value > & in ) const

inline

Addition.

Definition at line 327 of file LorentzTensor.h.

◆ operator-()

template<typename Value >

LorentzTensor< Value > ThePEG::Helicity::LorentzTensor< Value >::operator- ( const LorentzTensor< Value > & in ) const

inline

Subtraction.

Definition at line 337 of file LorentzTensor.h.

◆ outerProduct()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzTensor< Value >::outerProduct ( const LorentzTensor< ValueB > & ten ) const -> LorentzTensor<decltype(ten.xx().real()*this->xx().real())>

inline

Outer product with another tensor.

Definition at line 373 of file LorentzTensor.h.

◆ postDot() [1/2]

template<typename Value >

auto ThePEG::Helicity::LorentzTensor< Value >::postDot ( const Lorentz5Momentum & vec ) const -> LorentzVector<decltype(vec.x()*this->xx())>

inline

Second index dot product with momentum.

Definition at line 450 of file LorentzTensor.h.

◆ postDot() [2/2]

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzTensor< Value >::postDot ( const LorentzVector< complex< ValueB > > & vec ) const -> LorentzVector<decltype(vec.x()*this->xx())>

inline

Second index dot product with polarization vector.

Definition at line 415 of file LorentzTensor.h.

◆ preDot() [1/2]

template<typename Value >

auto ThePEG::Helicity::LorentzTensor< Value >::preDot ( const Lorentz5Momentum & vec ) const -> LorentzVector<decltype(vec.x()*this->xx())>

inline

First index dot product with momentum.

Definition at line 432 of file LorentzTensor.h.

◆ preDot() [2/2]

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzTensor< Value >::preDot ( const LorentzVector< complex< ValueB > > & vec ) const -> LorentzVector<decltype(vec.x()*this->xx())>

inline

Various dot products.

First index dot product with polarization vector

Definition at line 397 of file LorentzTensor.h.

◆ setTT()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setTT ( complex< Value > a )

inline

Set t,t component.

Definition at line 238 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::epsilon().

◆ setTX()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setTX ( complex< Value > a )

inline

Set t,x component.

Definition at line 178 of file LorentzTensor.h.

◆ setTY()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setTY ( complex< Value > a )

inline

Set t,y component.

Definition at line 198 of file LorentzTensor.h.

◆ setTZ()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setTZ ( complex< Value > a )

inline

Set t,z component.

Definition at line 218 of file LorentzTensor.h.

◆ setXT()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setXT ( complex< Value > a )

inline

Set x,t component.

Definition at line 223 of file LorentzTensor.h.

◆ setXX()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setXX ( complex< Value > a )

inline

Set x,x component.

Definition at line 163 of file LorentzTensor.h.

◆ setXY()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setXY ( complex< Value > a )

inline

Set x,y component.

Definition at line 183 of file LorentzTensor.h.

◆ setXZ()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setXZ ( complex< Value > a )

inline

Set x,z component.

Definition at line 203 of file LorentzTensor.h.

◆ setYT()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setYT ( complex< Value > a )

inline

Set y,t component.

Definition at line 228 of file LorentzTensor.h.

◆ setYX()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setYX ( complex< Value > a )

inline

Set y,x component.

Definition at line 168 of file LorentzTensor.h.

◆ setYY()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setYY ( complex< Value > a )

inline

Set y,y component.

Definition at line 188 of file LorentzTensor.h.

◆ setYZ()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setYZ ( complex< Value > a )

inline

Set y,z component.

Definition at line 208 of file LorentzTensor.h.

◆ setZT()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setZT ( complex< Value > a )

inline

Set z,t component.

Definition at line 233 of file LorentzTensor.h.

◆ setZX()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setZX ( complex< Value > a )

inline

Set z,x component.

Definition at line 173 of file LorentzTensor.h.

◆ setZY()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setZY ( complex< Value > a )

inline

Set z,y component.

Definition at line 193 of file LorentzTensor.h.

◆ setZZ()

template<typename Value >

void ThePEG::Helicity::LorentzTensor< Value >::setZZ ( complex< Value > a )

inline

Set z,z component.

Definition at line 213 of file LorentzTensor.h.

◆ trace()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::trace ( ) const

inline

Trace.

Definition at line 347 of file LorentzTensor.h.

◆ transform()

template<typename Value >

LorentzTensor & ThePEG::Helicity::LorentzTensor< Value >::transform ( const SpinOneLorentzRotation & r )

inline

General Lorentz transformation.

Definition at line 274 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::TensorWaveFunction::transform().

◆ tt()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::tt ( ) const

inline

Get t,t component.

Definition at line 158 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::tt().

◆ tx()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::tx ( ) const

inline

Get t,x component.

Definition at line 98 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::tx().

◆ ty()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::ty ( ) const

inline

Get t,y component.

Definition at line 118 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::ty().

◆ tz()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::tz ( ) const

inline

Get t,z component.

Definition at line 138 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::tz().

◆ xt()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::xt ( ) const

inline

Get x,t component.

Definition at line 143 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::xt().

◆ xx()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::xx ( ) const

inline

Get x,x component.

Definition at line 84 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::xx().

◆ xy()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::xy ( ) const

inline

Get x,y component.

Definition at line 103 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::xy().

◆ xz()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::xz ( ) const

inline

Get x,z component.

Definition at line 123 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::xz().

◆ yt()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::yt ( ) const

inline

Get y,t component.

Definition at line 148 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::yt().

◆ yx()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::yx ( ) const

inline

Get y,x component.

Definition at line 89 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::yx().

◆ yy()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::yy ( ) const

inline

Get y,y component.

Definition at line 108 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::yy().

◆ yz()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::yz ( ) const

inline

Get y,z component.

Definition at line 128 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::yz().

◆ zt()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::zt ( ) const

inline

Get z,t component.

Definition at line 153 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::zt().

◆ zx()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::zx ( ) const

inline

Get z,x component.

Definition at line 93 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::zx().

◆ zy()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::zy ( ) const

inline

Get z,y component.

Definition at line 113 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::zy().

◆ zz()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzTensor< Value >::zz ( ) const

inline

Get z,z component.

Definition at line 133 of file LorentzTensor.h.

Referenced by ThePEG::Helicity::LorentzTensor< Value >::LorentzTensor(), ThePEG::Helicity::LorentzTensor< Value >::operator+(), ThePEG::Helicity::LorentzTensor< Value >::operator-(), and ThePEG::Helicity::TensorWaveFunction::zz().

Friends And Related Function Documentation

◆ operator*

template<typename Value >

template<typename T , typename U >

auto operator*	(	const LorentzTensor< T > &	t,
		const LorentzTensor< U > &	u
	)		-> decltype(t.xx()*u.xx())

friend

Scalar product with other tensor.

Definition at line 550 of file LorentzTensor.h.

Member Data Documentation

◆ _tensor

template<typename Value >

std::array<std::array<complex<Value>,4>,4> ThePEG::Helicity::LorentzTensor< Value >::_tensor

private

The components.

Definition at line 470 of file LorentzTensor.h.

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

LorentzTensor.h

Public Member Functions

Arithmetic operators.

Detailed Description

Constructor & Destructor Documentation

◆ LorentzTensor() [1/2]

◆ LorentzTensor() [2/2]

Member Function Documentation

◆ boost()

◆ conjugate()

◆ innerProduct()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+()

◆ operator-()

◆ outerProduct()

◆ postDot() [1/2]

◆ postDot() [2/2]

◆ preDot() [1/2]

◆ preDot() [2/2]

◆ setTT()

◆ setTX()

◆ setTY()

◆ setTZ()

◆ setXT()

◆ setXX()

◆ setXY()

◆ setXZ()

◆ setYT()

◆ setYX()

◆ setYY()

◆ setYZ()

◆ setZT()

◆ setZX()

◆ setZY()

◆ setZZ()

◆ trace()

◆ transform()

◆ tt()

◆ tx()

◆ ty()

◆ tz()

◆ xt()

◆ xx()

◆ xy()

◆ xz()

◆ yt()

◆ yx()

◆ yy()

◆ yz()

◆ zt()

◆ zx()

◆ zy()

◆ zz()

Friends And Related Function Documentation

◆ operator*

Member Data Documentation

◆ _tensor