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

#include <LorentzSpinor.h>

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

Public Member Functions
template<typename U >
	LorentzSpinor (const LorentzSpinor< U > &other)

template<typename ValueB >
auto	sigma (const LorentzSpinorBar< ValueB > &fb) const -> LorentzTensor< decltype(fb.s1() *this->s1())>
	Calculate the product with $\sigma^{\mu\nu}$ , i.e. More...

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.

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 $u_c=C\bar{u}^T$ . More...

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 .

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 $\bar{f}\gamma^\mu P_Lf$ . More...

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

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

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. More...

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

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

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

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

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. More...

Private Attributes
SpinorType	_type
	Type of spinor.

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

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.

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(), and ThePEG::Helicity::LorentzSpinor< double >::setS4().

◆ 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, .
right	The right coupling, .

Definition at line 392 of file LorentzSpinor.h.

◆ 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, .
right	The right coupling, .

Definition at line 471 of file LorentzSpinor.h.

◆ 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.

◆ 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.

◆ 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.

◆ sigma()

template<typename Value>

template<typename ValueB >

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

inline

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

$\bar{f}\sigma^{\mu\nu}f$

Definition at line 485 of file LorentzSpinor.h.

◆ 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.

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

LorentzSpinor.h

Public Member Functions

Private Attributes

Detailed Description

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

Member Function Documentation

◆ conjugate()

◆ generalCurrent()

◆ generalScalar()

◆ leftCurrent()

◆ leftScalar()

◆ pseudoScalar()

◆ rightCurrent()

◆ rightScalar()

◆ scalar()

◆ sigma()

◆ vectorCurrent()

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