The LorentzRSSpinor class is designed to store a Rarita-Schwinger spinor for a spin-3/2 particle. More...

#include <LorentzRSSpinor.h>

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

Public Member Functions
template<typename ValueB >
auto	generalScalar (LorentzRSSpinorBar< ValueB > &fbar, Complex left, Complex right) -> decltype(left fbar(3, 0) this->ts1())
	Scalar product $\bar{f}^\alpha(c_LP_L+c_RP_R)f_\alpha$ for general couplings. More...

template<typename ValueB >
auto	generalCurrent (LorentzSpinorBar< ValueB > &fbar, Complex left, Complex right) -> LorentzVector< decltype(left fbar.s1() this->ts1())>
	Current $\bar{f}(c_LP_L+c_RP_R)f^\alpha$ for general couplings. More...

Standard constructors.
	LorentzRSSpinor (SpinorType t=SpinorType::unknown)
	Default zero constructor, optionally specifying t, the type.

	LorentzRSSpinor (complex< Value > a1, complex< Value > b1, complex< Value > c1, complex< Value > d1, complex< Value > a2, complex< Value > b2, complex< Value > c2, complex< Value > d2, complex< Value > a3, complex< Value > b3, complex< Value > c3, complex< Value > d3, complex< Value > a4, complex< Value > b4, complex< Value > c4, complex< Value > d4, SpinorType t=SpinorType::unknown)
	Constructor with complex numbers specifying the components, optionally specifying t, the type.

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

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

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

complex< Value >	xs1 () const
	Get first spinor component for the x vector.

complex< Value >	xs2 () const
	Get second spinor component for the x vector.

complex< Value >	xs3 () const
	Get third spinor component for the x vector.

complex< Value >	xs4 () const
	Get fourth spinor component for the x vector.

complex< Value >	ys1 () const
	Get first spinor component for the y vector.

complex< Value >	ys2 () const
	Get second spinor component for the y vector.

complex< Value >	ys3 () const
	Get third spinor component for the y vector.

complex< Value >	ys4 () const
	Get fourth spinor component for the y vector.

complex< Value >	zs1 () const
	Get first spinor component for the z vector.

complex< Value >	zs2 () const
	Get second spinor component for the z vector.

complex< Value >	zs3 () const
	Get third spinor component for the z vector.

complex< Value >	zs4 () const
	Get fourth spinor component for the z vector.

complex< Value >	ts1 () const
	Get first spinor component for the t vector.

complex< Value >	ts2 () const
	Get second spinor component for the t vector.

complex< Value >	ts3 () const
	Get third spinor component for the t vector.

complex< Value >	ts4 () const
	Get fourth spinor component for the t vector.

void	setXS1 (complex< Value > in)
	Set first spinor component for the x vector.

void	setXS2 (complex< Value > in)
	Set second spinor component for the x vector.

void	setXS3 (complex< Value > in)
	Set third spinor component for the x vector.

void	setXS4 (complex< Value > in)
	Set fourth spinor component for the x vector.

void	setYS1 (complex< Value > in)
	Set first spinor component for the y vector.

void	setYS2 (complex< Value > in)
	Set second spinor component for the y vector.

void	setYS3 (complex< Value > in)
	Set third spinor component for the y vector.

void	setYS4 (complex< Value > in)
	Set fourth spinor component for the y vector.

void	setZS1 (complex< Value > in)
	Set first spinor component for the z vector.

void	setZS2 (complex< Value > in)
	Set second spinor component for the z vector.

void	setZS3 (complex< Value > in)
	Set third spinor component for the z vector.

void	setZS4 (complex< Value > in)
	Set fourth spinor component for the z vector.

void	setTS1 (complex< Value > in)
	Set first spinor component for the t vector.

void	setTS2 (complex< Value > in)
	Set second spinor component for the t vector.

void	setTS3 (complex< Value > in)
	Set third spinor component for the t vector.

void	setTS4 (complex< Value > in)
	Set fourth spinor component for the t vector.

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

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

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

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

Arithmetic operators.
LorentzSpinor< Value >	dot (const LorentzPolarizationVector &vec) const
	dot product with a polarization vector

LorentzSpinor< Value >	dot (const LorentzMomentum &invec) const
	dot product with a 4-vector

Transformations.
LorentzRSSpinorBar< Value >	bar () const
	return the barred spinor

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

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

LorentzRSSpinor &	transform (const LorentzRotation &)
	General transform.

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

Private Attributes
SpinorType	_type
	Type of spinor.

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

Detailed Description

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

The LorentzRSSpinor class is designed to store a Rarita-Schwinger spinor for a spin-3/2 particle.

In addition to storing the components of the spinor information is stored on 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 LorentzRSSpinorBar class is also provided to store the barred spinor.

See also: HelicityDefinitions; LorentzRSSpinorBar

Author: Peter Richardson

Definition at line 73 of file LorentzRSSpinor.h.

Member Function Documentation

◆ generalCurrent()

template<typename Value>

template<typename ValueB >

auto ThePEG::Helicity::LorentzRSSpinor< Value >::generalCurrent	(	LorentzSpinorBar< ValueB > &	fbar,
		Complex	left,
		Complex	right
	)		-> LorentzVector<decltype(leftfbar.s1()this->ts1())>

inline

Current $\bar{f}(c_LP_L+c_RP_R)f^\alpha$ for general couplings.

Parameters

fbar	The barred spinor
left	The left-handed coupling, .
right	The right-handed coupling, .

Definition at line 419 of file LorentzRSSpinor.h.

◆ generalScalar()

template<typename Value>

template<typename ValueB >

auto ThePEG::Helicity::LorentzRSSpinor< Value >::generalScalar	(	LorentzRSSpinorBar< ValueB > &	fbar,
		Complex	left,
		Complex	right
	)		-> decltype(leftfbar(3,0)this->ts1())

inline

Scalar product $\bar{f}^\alpha(c_LP_L+c_RP_R)f_\alpha$ for general couplings.

Parameters

fbar	The barred spinor
left	The left-handed coupling, .
right	The right-handed coupling, .

Definition at line 395 of file LorentzRSSpinor.h.

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

LorentzRSSpinor.h

Public Member Functions

Private Attributes

Detailed Description

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

Member Function Documentation

◆ generalCurrent()

◆ generalScalar()

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