The LorentzSpinor class is designed to store a spinor. More...

#include <LorentzSpinor.h>

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

Public Member Functions
Standard constructors.
	LorentzSpinor (SpinorType t=SpinorType::unknown)
	Default zero constructor, optionally specifying t, the type.

	LorentzSpinor (complex< Value > a, complex< Value > b, complex< Value > c, complex< Value > d, SpinorType s=SpinorType::unknown)
	Constructor with complex numbers specifying the components, optionally specifying s, the type.

template<typename U >
	LorentzSpinor (const LorentzSpinor< U > &other)

Access the components.
complex< Value >	operator[] (int i) const
	Subscript operator to return spinor components.

complex< Value >	operator() (int i) const
	Subscript operator to return spinor components.

complex< Value > &	operator() (int i)
	Set components by index.

complex< Value > &	operator[] (int i)
	Set components by index.

complex< Value >	s1 () const
	Get first component.

complex< Value >	s2 () const
	Get second component.

complex< Value >	s3 () const
	Get third component.

complex< Value >	s4 () const
	Get fourth component.

void	setS1 (complex< Value > in)
	Set first component.

void	setS2 (complex< Value > in)
	Set second component.

void	setS3 (complex< Value > in)
	Set third component.

void	setS4 (complex< Value > in)
	Set fourth component.

Mathematical assignment operators.
template<typename ValueB >
LorentzSpinor< Value > &	operator+= (const LorentzSpinor< ValueB > &a)

template<typename ValueB >
LorentzSpinor< Value > &	operator-= (const LorentzSpinor< ValueB > &a)

LorentzSpinor< Value > &	operator*= (double a)

LorentzSpinor< Value > &	operator/= (double a)

Transformations.
LorentzSpinorBar< Value >	bar () const
	Return the barred spinor.

LorentzSpinor	conjugate () const
	Return the conjugated spinor \(u_c=C\bar{u}^T\).

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

LorentzSpinor &	boost (const Boost &)
	Standard Lorentz boost specifying the beta vector.

LorentzSpinor &	transform (const SpinHalfLorentzRotation &)
	General Lorentz transformation.

LorentzSpinor &	transform (const LorentzRotation &r)
	General Lorentz transformation.

Functions related to type.
SpinorType	Type () const
	Return the type of the spinor.

Functions to apply the projection operator
template<typename ValueB >
auto	projectionOperator (const LorentzVector< ValueB > &p, const ValueB &m) const -> LorentzSpinor< decltype(m *Value())>
	Apply \(p\!\!\!\!\!\not\,\,\,+m\).

LorentzSpinor	helicityProjectionOperator (const Complex &gL, const Complex &gR) const
	Apply \(g^LP_L+g^RP_R\).

Functions to calculate certain currents.
template<typename ValueB >
auto	slash (const LorentzVector< ValueB > &p) const -> LorentzSpinor< decltype(p.t() *Value())>
	Apply \(p\!\!\!\!\!\not\).

template<typename ValueB >
auto	slash (const LorentzVector< complex< ValueB > > &p) const -> LorentzSpinor< decltype(ValueB() *Value())>
	Apply \(p\!\!\!\!\!\not\).

template<typename ValueB >
auto	leftCurrent (const LorentzSpinorBar< ValueB > &fb) const -> LorentzVector< decltype(fb.s3() *this->s2())>
	Calculate the left-handed current \(\bar{f}\gamma^\mu P_Lf\).

template<typename ValueB >
auto	rightCurrent (const LorentzSpinorBar< ValueB > &fb) const -> LorentzVector< decltype(fb.s1() *this->s4())>
	Calculate the right-handed current \(\bar{f}\gamma^\mu P_Rf\).

template<typename ValueB >
auto	vectorCurrent (const LorentzSpinorBar< ValueB > &fb) const -> LorentzVector< decltype(fb.s1() *this->s4())>
	Calculate the vector current \(\bar{f}\gamma^\mu f\).

template<typename ValueB >
auto	generalCurrent (const LorentzSpinorBar< ValueB > &fb, Complex left, Complex right) const -> LorentzVector< decltype(fb.s3() *this->s2())>
	Calculate a general current with arbitary left and right couplings, i.e.

Functions to calculate certain scalars.
SpinorType	_type
	Type of spinor.

std::array< complex< Value >, 4 >	_spin
	Storage of the components.

template<typename ValueB >
auto	leftScalar (const LorentzSpinorBar< ValueB > &fb) const -> decltype(fb.s1() *this->s1())
	Calculate the left-handed scalar \(\bar{f}P_Lf\).

template<typename ValueB >
auto	rightScalar (const LorentzSpinorBar< ValueB > &fb) const -> decltype(fb.s3() *this->s3())
	Calculate the right-handed scalar \(\bar{f}P_Rf\).

template<typename ValueB >
auto	scalar (const LorentzSpinorBar< ValueB > &fb) const -> decltype(fb.s1() *this->s1())
	Calculate the scalar \(\bar{f}f\).

template<typename ValueB >
auto	pseudoScalar (const LorentzSpinorBar< ValueB > &fb) const -> decltype(fb.s1() *this->s1())
	Calculate the pseudoscalar \(\bar{f}\gamma_5f\).

template<typename ValueB >
auto	generalScalar (const LorentzSpinorBar< ValueB > &fb, Complex left, Complex right) const -> decltype(left fb.s1() this->s1())
	Calculate a general scalar product with arbitary left and right couplings, i.e.

template<typename ValueB >
auto	sigma (const LorentzSpinorBar< ValueB > &fb) const -> LorentzTensor< decltype(ValueB() *Value())>
	Calculate the product with \(\sigma^{\mu\nu}\), i.e.

Detailed Description

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

The LorentzSpinor class is designed to store a spinor.

In addition to storing the components of the spinor, information is stored on the representation of the type of spinor, for example u or v type.

At the moment only one choice of the Dirac matrix representation is supported. For high-energy calculations the choice made by the HELAS collaboration is more efficient for numerical calculations. In this representation

\[ \gamma_{i=1,2,3}=\left(\begin{array}{cc} 0 & \sigma_i \\ -\sigma_i & 0 \end{array}\right) \quad \gamma_0=\left(\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right) \quad \gamma_5=\left(\begin{array}{cc} -1 & 0 \\ 0 & 1 \end{array}\right) \]

The type of the spinor is also stored using the SpinorType enumeration. There are three types supported SpinorType::u, SpinorType::v, SpinorType::unknown. This information is intended mainly for use in the case of Majorana particles where matrix elements can be calculated with either u or v type spinors and knowledge of which was used will be needed in order to give the correct correlations. The SpinorType::unknowne is intended for cases where either the spinor for an off-shell line in a matrix element calculation or the information is genuinely unknown.

The LorentzSpinorBar class is also provided to store the barred spinor.

See also: LorentzSpinorBar

Author: Peter Richardson

Definition at line 71 of file LorentzSpinor.h.

Constructor & Destructor Documentation

◆ LorentzSpinor() [1/3]

template<typename Value >

ThePEG::Helicity::LorentzSpinor< Value >::LorentzSpinor ( SpinorType t = SpinorType::unknown )

inline

Default zero constructor, optionally specifying t, the type.

Definition at line 79 of file LorentzSpinor.h.

◆ LorentzSpinor() [2/3]

template<typename Value >

ThePEG::Helicity::LorentzSpinor< Value >::LorentzSpinor	(	complex< Value >	a,
		complex< Value >	b,
		complex< Value >	c,
		complex< Value >	d,
		SpinorType	s = `SpinorType::unknown`
	)

inline

Constructor with complex numbers specifying the components, optionally specifying s, the type.

Definition at line 85 of file LorentzSpinor.h.

◆ LorentzSpinor() [3/3]

template<typename Value >

template<typename U >

ThePEG::Helicity::LorentzSpinor< Value >::LorentzSpinor ( const LorentzSpinor< U > & other )

inline

Definition at line 91 of file LorentzSpinor.h.

Member Function Documentation

◆ conjugate()

template<typename Value >

LorentzSpinor ThePEG::Helicity::LorentzSpinor< Value >::conjugate ( ) const

Return the conjugated spinor \(u_c=C\bar{u}^T\).

This operation transforms u-spinors to v-spinors and vice-versa and is required when dealing with majorana particles.

Referenced by ThePEG::Helicity::SpinorWaveFunction::conjugate().

◆ generalCurrent()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::generalCurrent	(	const LorentzSpinorBar< ValueB > &	fb,
		Complex	left,
		Complex	right
	)		const -> LorentzVector<decltype(fb.s3()*this->s2())>

inline

Calculate a general current with arbitary left and right couplings, i.e.

\(\bar{f}\gamma^\mu(c_lP_L+c_RP_R)f\)

Parameters

fb	The barred spinor.
left	The left coupling, \(c_L\).
right	The right coupling, \(c_R\).

Definition at line 392 of file LorentzSpinor.h.

References ThePEG::left(), and ThePEG::right().

◆ generalScalar()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::generalScalar	(	const LorentzSpinorBar< ValueB > &	fb,
		Complex	left,
		Complex	right
	)		const -> decltype(leftfb.s1()this->s1())

inline

Calculate a general scalar product with arbitary left and right couplings, i.e.

\(\bar{f}c_lP_L+c_RP_Rf\)

Parameters

fb	The barred spinor.
left	The left coupling, \(c_L\).
right	The right coupling, \(c_R\).

Definition at line 471 of file LorentzSpinor.h.

References ThePEG::left(), and ThePEG::right().

◆ helicityProjectionOperator()

template<typename Value >

LorentzSpinor ThePEG::Helicity::LorentzSpinor< Value >::helicityProjectionOperator	(	const Complex &	gL,
		const Complex &	gR
	)		const

inline

Apply \(g^LP_L+g^RP_R\).

Definition at line 269 of file LorentzSpinor.h.

References ThePEG::Helicity::LorentzSpinor< Value >::setS1(), ThePEG::Helicity::LorentzSpinor< Value >::setS2(), ThePEG::Helicity::LorentzSpinor< Value >::setS3(), and ThePEG::Helicity::LorentzSpinor< Value >::setS4().

◆ leftCurrent()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::leftCurrent ( const LorentzSpinorBar< ValueB > & fb ) const -> LorentzVector<decltype(fb.s3()*this->s2())>

inline

Calculate the left-handed current \(\bar{f}\gamma^\mu P_Lf\).

Parameters

fb	The barred spinor.

Definition at line 327 of file LorentzSpinor.h.

◆ leftScalar()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::leftScalar ( const LorentzSpinorBar< ValueB > & fb ) const -> decltype(fb.s1()*this->s1())

inline

Calculate the left-handed scalar \(\bar{f}P_Lf\).

Parameters

fb	The barred spinor.

Definition at line 422 of file LorentzSpinor.h.

◆ operator()() [1/2]

template<typename Value >

complex< Value > & ThePEG::Helicity::LorentzSpinor< Value >::operator() ( int i )

inline

Set components by index.

Definition at line 115 of file LorentzSpinor.h.

◆ operator()() [2/2]

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzSpinor< Value >::operator() ( int i ) const

inline

Subscript operator to return spinor components.

Definition at line 107 of file LorentzSpinor.h.

◆ operator*=()

template<typename Value >

LorentzSpinor< Value > & ThePEG::Helicity::LorentzSpinor< Value >::operator*= ( double a )

inline

Definition at line 183 of file LorentzSpinor.h.

◆ operator+=()

template<typename Value >

template<typename ValueB >

LorentzSpinor< Value > & ThePEG::Helicity::LorentzSpinor< Value >::operator+= ( const LorentzSpinor< ValueB > & a )

inline

Definition at line 172 of file LorentzSpinor.h.

◆ operator-=()

template<typename Value >

template<typename ValueB >

LorentzSpinor< Value > & ThePEG::Helicity::LorentzSpinor< Value >::operator-= ( const LorentzSpinor< ValueB > & a )

inline

Definition at line 178 of file LorentzSpinor.h.

◆ operator/=()

template<typename Value >

LorentzSpinor< Value > & ThePEG::Helicity::LorentzSpinor< Value >::operator/= ( double a )

inline

Definition at line 188 of file LorentzSpinor.h.

◆ operator[]() [1/2]

template<typename Value >

complex< Value > & ThePEG::Helicity::LorentzSpinor< Value >::operator[] ( int i )

inline

Set components by index.

Definition at line 123 of file LorentzSpinor.h.

◆ operator[]() [2/2]

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzSpinor< Value >::operator[] ( int i ) const

inline

Subscript operator to return spinor components.

Definition at line 99 of file LorentzSpinor.h.

◆ projectionOperator()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::projectionOperator	(	const LorentzVector< ValueB > &	p,
		const ValueB &	m
	)		const -> LorentzSpinor<decltype(m*Value())>

inline

Apply \(p\!\!\!\!\!\not\,\,\,+m\).

Definition at line 248 of file LorentzSpinor.h.

◆ pseudoScalar()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::pseudoScalar ( const LorentzSpinorBar< ValueB > & fb ) const -> decltype(fb.s1()*this->s1())

inline

Calculate the pseudoscalar \(\bar{f}\gamma_5f\).

Parameters

fb	The barred spinor.

Definition at line 456 of file LorentzSpinor.h.

◆ rightCurrent()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::rightCurrent ( const LorentzSpinorBar< ValueB > & fb ) const -> LorentzVector<decltype(fb.s1()*this->s4())>

inline

Calculate the right-handed current \(\bar{f}\gamma^\mu P_Rf\).

Parameters

fb	The barred spinor.

Definition at line 347 of file LorentzSpinor.h.

◆ rightScalar()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::rightScalar ( const LorentzSpinorBar< ValueB > & fb ) const -> decltype(fb.s3()*this->s3())

inline

Calculate the right-handed scalar \(\bar{f}P_Rf\).

Parameters

fb	The barred spinor.

Definition at line 433 of file LorentzSpinor.h.

◆ s1()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzSpinor< Value >::s1 ( ) const

inline

Get first component.

Definition at line 131 of file LorentzSpinor.h.

Referenced by ThePEG::Helicity::SpinorWaveFunction::s1().

◆ s2()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzSpinor< Value >::s2 ( ) const

inline

Get second component.

Definition at line 136 of file LorentzSpinor.h.

Referenced by ThePEG::Helicity::SpinorWaveFunction::s2().

◆ s3()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzSpinor< Value >::s3 ( ) const

inline

Get third component.

Definition at line 141 of file LorentzSpinor.h.

Referenced by ThePEG::Helicity::SpinorWaveFunction::s3().

◆ s4()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzSpinor< Value >::s4 ( ) const

inline

Get fourth component.

Definition at line 146 of file LorentzSpinor.h.

Referenced by ThePEG::Helicity::SpinorWaveFunction::s4().

◆ scalar()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::scalar ( const LorentzSpinorBar< ValueB > & fb ) const -> decltype(fb.s1()*this->s1())

inline

Calculate the scalar \(\bar{f}f\).

Parameters

fb	The barred spinor.

Definition at line 444 of file LorentzSpinor.h.

◆ setS1()

template<typename Value >

void ThePEG::Helicity::LorentzSpinor< Value >::setS1 ( complex< Value > in )

inline

Set first component.

Definition at line 151 of file LorentzSpinor.h.

Referenced by ThePEG::Helicity::LorentzSpinor< Value >::helicityProjectionOperator().

◆ setS2()

template<typename Value >

void ThePEG::Helicity::LorentzSpinor< Value >::setS2 ( complex< Value > in )

inline

Set second component.

Definition at line 156 of file LorentzSpinor.h.

Referenced by ThePEG::Helicity::LorentzSpinor< Value >::helicityProjectionOperator().

◆ setS3()

template<typename Value >

void ThePEG::Helicity::LorentzSpinor< Value >::setS3 ( complex< Value > in )

inline

Set third component.

Definition at line 161 of file LorentzSpinor.h.

Referenced by ThePEG::Helicity::LorentzSpinor< Value >::helicityProjectionOperator().

◆ setS4()

template<typename Value >

void ThePEG::Helicity::LorentzSpinor< Value >::setS4 ( complex< Value > in )

inline

Set fourth component.

Definition at line 166 of file LorentzSpinor.h.

Referenced by ThePEG::Helicity::LorentzSpinor< Value >::helicityProjectionOperator().

◆ sigma()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::sigma ( const LorentzSpinorBar< ValueB > & fb ) const -> LorentzTensor<decltype(ValueB()*Value())>

inline

Calculate the product with \(\sigma^{\mu\nu}\), i.e.

\(\bar{f}\sigma^{\mu\nu}f\)

Definition at line 485 of file LorentzSpinor.h.

References ThePEG::ZERO.

◆ slash() [1/2]

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::slash ( const LorentzVector< complex< ValueB > > & p ) const -> LorentzSpinor<decltype(ValueB()*Value())>

inline

Apply \(p\!\!\!\!\!\not\).

Definition at line 306 of file LorentzSpinor.h.

◆ slash() [2/2]

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::slash ( const LorentzVector< ValueB > & p ) const -> LorentzSpinor<decltype(p.t()*Value())>

inline

Apply \(p\!\!\!\!\!\not\).

Definition at line 286 of file LorentzSpinor.h.

◆ transform()

template<typename Value >

LorentzSpinor & ThePEG::Helicity::LorentzSpinor< Value >::transform ( const LorentzRotation & r )

inline

General Lorentz transformation.

Definition at line 226 of file LorentzSpinor.h.

References ThePEG::LorentzRotation::half().

◆ Type()

template<typename Value >

SpinorType ThePEG::Helicity::LorentzSpinor< Value >::Type ( ) const

inline

Return the type of the spinor.

Definition at line 237 of file LorentzSpinor.h.

Referenced by ThePEG::Helicity::SpinorWaveFunction::dimensionedWf().

◆ vectorCurrent()

template<typename Value >

template<typename ValueB >

auto ThePEG::Helicity::LorentzSpinor< Value >::vectorCurrent ( const LorentzSpinorBar< ValueB > & fb ) const -> LorentzVector<decltype(fb.s1()*this->s4())>

inline

Calculate the vector current \(\bar{f}\gamma^\mu f\).

Parameters

fb	The barred spinor.

Definition at line 367 of file LorentzSpinor.h.

Member Data Documentation

◆ _spin

template<typename Value >

std::array<complex<Value>,4> ThePEG::Helicity::LorentzSpinor< Value >::_spin

private

Storage of the components.

Definition at line 524 of file LorentzSpinor.h.

◆ _type

template<typename Value >

SpinorType ThePEG::Helicity::LorentzSpinor< Value >::_type

private

Type of spinor.

Definition at line 519 of file LorentzSpinor.h.

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

LorentzSpinor.h

Public Member Functions

Functions to calculate certain scalars.

Detailed Description

Constructor & Destructor Documentation

◆ LorentzSpinor() [1/3]

◆ LorentzSpinor() [2/3]

◆ LorentzSpinor() [3/3]

Member Function Documentation

◆ conjugate()

◆ generalCurrent()

◆ generalScalar()

◆ helicityProjectionOperator()

◆ leftCurrent()

◆ leftScalar()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ projectionOperator()

◆ pseudoScalar()

◆ rightCurrent()

◆ rightScalar()

◆ s1()

◆ s2()

◆ s3()

◆ s4()

◆ scalar()

◆ setS1()

◆ setS2()

◆ setS3()

◆ setS4()

◆ sigma()

◆ slash() [1/2]

◆ slash() [2/2]

◆ transform()

◆ Type()

◆ vectorCurrent()

Member Data Documentation

◆ _spin

◆ _type