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
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
	Type of spinor.

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

SpinorType	Type () const
	Return the type of the spinor.

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.

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.

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.

Constructor & Destructor Documentation

◆ LorentzRSSpinor() [1/3]

template<typename Value >

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

inline

Default zero constructor, optionally specifying t, the type.

Definition at line 82 of file LorentzRSSpinor.h.

◆ LorentzRSSpinor() [2/3]

template<typename Value >

ThePEG::Helicity::LorentzRSSpinor< Value >::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`
	)

inline

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

Definition at line 88 of file LorentzRSSpinor.h.

◆ LorentzRSSpinor() [3/3]

template<typename Value >

template<typename U >

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

inline

Definition at line 104 of file LorentzRSSpinor.h.

Member Function Documentation

◆ dot() [1/2]

template<typename Value >

LorentzSpinor< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::dot ( const LorentzMomentum & invec ) const

inline

dot product with a 4-vector

Definition at line 342 of file LorentzRSSpinor.h.

◆ dot() [2/2]

template<typename Value >

LorentzSpinor< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::dot ( const LorentzPolarizationVector & vec ) const

inline

dot product with a polarization vector

Definition at line 325 of file LorentzRSSpinor.h.

◆ 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, \(c_L\).
right	The right-handed coupling, \(c_R\).

Definition at line 419 of file LorentzRSSpinor.h.

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

◆ 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, \(c_L\).
right	The right-handed coupling, \(c_R\).

Definition at line 395 of file LorentzRSSpinor.h.

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

◆ operator()() [1/2]

template<typename Value >

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

inline

Set components by index.

Definition at line 121 of file LorentzRSSpinor.h.

◆ operator()() [2/2]

template<typename Value >

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

inline

Subscript operator to return spinor components.

Definition at line 113 of file LorentzRSSpinor.h.

◆ operator*=()

template<typename Value >

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

inline

Definition at line 305 of file LorentzRSSpinor.h.

◆ operator+=()

template<typename Value >

template<typename ValueB >

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

inline

Definition at line 290 of file LorentzRSSpinor.h.

◆ operator-=()

template<typename Value >

template<typename ValueB >

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

inline

Definition at line 298 of file LorentzRSSpinor.h.

◆ operator/=()

template<typename Value >

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

inline

Definition at line 312 of file LorentzRSSpinor.h.

◆ setTS1()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setTS1 ( complex< Value > in )

inline

Set first spinor component for the t vector.

Definition at line 269 of file LorentzRSSpinor.h.

◆ setTS2()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setTS2 ( complex< Value > in )

inline

Set second spinor component for the t vector.

Definition at line 274 of file LorentzRSSpinor.h.

◆ setTS3()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setTS3 ( complex< Value > in )

inline

Set third spinor component for the t vector.

Definition at line 279 of file LorentzRSSpinor.h.

◆ setTS4()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setTS4 ( complex< Value > in )

inline

Set fourth spinor component for the t vector.

Definition at line 284 of file LorentzRSSpinor.h.

◆ setXS1()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setXS1 ( complex< Value > in )

inline

Set first spinor component for the x vector.

Definition at line 209 of file LorentzRSSpinor.h.

◆ setXS2()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setXS2 ( complex< Value > in )

inline

Set second spinor component for the x vector.

Definition at line 214 of file LorentzRSSpinor.h.

◆ setXS3()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setXS3 ( complex< Value > in )

inline

Set third spinor component for the x vector.

Definition at line 219 of file LorentzRSSpinor.h.

◆ setXS4()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setXS4 ( complex< Value > in )

inline

Set fourth spinor component for the x vector.

Definition at line 224 of file LorentzRSSpinor.h.

◆ setYS1()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setYS1 ( complex< Value > in )

inline

Set first spinor component for the y vector.

Definition at line 229 of file LorentzRSSpinor.h.

◆ setYS2()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setYS2 ( complex< Value > in )

inline

Set second spinor component for the y vector.

Definition at line 234 of file LorentzRSSpinor.h.

◆ setYS3()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setYS3 ( complex< Value > in )

inline

Set third spinor component for the y vector.

Definition at line 239 of file LorentzRSSpinor.h.

◆ setYS4()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setYS4 ( complex< Value > in )

inline

Set fourth spinor component for the y vector.

Definition at line 244 of file LorentzRSSpinor.h.

◆ setZS1()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setZS1 ( complex< Value > in )

inline

Set first spinor component for the z vector.

Definition at line 249 of file LorentzRSSpinor.h.

◆ setZS2()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setZS2 ( complex< Value > in )

inline

Set second spinor component for the z vector.

Definition at line 254 of file LorentzRSSpinor.h.

◆ setZS3()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setZS3 ( complex< Value > in )

inline

Set third spinor component for the z vector.

Definition at line 259 of file LorentzRSSpinor.h.

◆ setZS4()

template<typename Value >

void ThePEG::Helicity::LorentzRSSpinor< Value >::setZS4 ( complex< Value > in )

inline

Set fourth spinor component for the z vector.

Definition at line 264 of file LorentzRSSpinor.h.

◆ ts1()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::ts1 ( ) const

inline

Get first spinor component for the t vector.

Definition at line 189 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::ts1().

◆ ts2()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::ts2 ( ) const

inline

Get second spinor component for the t vector.

Definition at line 194 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::ts2().

◆ ts3()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::ts3 ( ) const

inline

Get third spinor component for the t vector.

Definition at line 199 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::ts3().

◆ ts4()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::ts4 ( ) const

inline

Get fourth spinor component for the t vector.

Definition at line 204 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::ts4().

◆ Type()

template<typename Value >

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

inline

Return the type of the spinor.

Definition at line 385 of file LorentzRSSpinor.h.

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

◆ xs1()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::xs1 ( ) const

inline

Get first spinor component for the x vector.

Definition at line 129 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::xs1().

◆ xs2()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::xs2 ( ) const

inline

Get second spinor component for the x vector.

Definition at line 134 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::xs2().

◆ xs3()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::xs3 ( ) const

inline

Get third spinor component for the x vector.

Definition at line 139 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::xs3().

◆ xs4()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::xs4 ( ) const

inline

Get fourth spinor component for the x vector.

Definition at line 144 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::xs4().

◆ ys1()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::ys1 ( ) const

inline

Get first spinor component for the y vector.

Definition at line 149 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::ys1().

◆ ys2()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::ys2 ( ) const

inline

Get second spinor component for the y vector.

Definition at line 154 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::ys2().

◆ ys3()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::ys3 ( ) const

inline

Get third spinor component for the y vector.

Definition at line 159 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::ys3().

◆ ys4()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::ys4 ( ) const

inline

Get fourth spinor component for the y vector.

Definition at line 164 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::ys4().

◆ zs1()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::zs1 ( ) const

inline

Get first spinor component for the z vector.

Definition at line 169 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::zs1().

◆ zs2()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::zs2 ( ) const

inline

Get second spinor component for the z vector.

Definition at line 174 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::zs2().

◆ zs3()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::zs3 ( ) const

inline

Get third spinor component for the z vector.

Definition at line 179 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::zs3().

◆ zs4()

template<typename Value >

complex< Value > ThePEG::Helicity::LorentzRSSpinor< Value >::zs4 ( ) const

inline

Get fourth spinor component for the z vector.

Definition at line 184 of file LorentzRSSpinor.h.

Referenced by ThePEG::Helicity::RSSpinorWaveFunction::zs4().

Member Data Documentation

◆ _spin

template<typename Value >

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

private

Storage of the components.

Definition at line 441 of file LorentzRSSpinor.h.

◆ _type

template<typename Value >

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

private

Type of spinor.

Definition at line 436 of file LorentzRSSpinor.h.

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

LorentzRSSpinor.h

Public Member Functions

Functions related to type.

Detailed Description

Constructor & Destructor Documentation

◆ LorentzRSSpinor() [1/3]

◆ LorentzRSSpinor() [2/3]

◆ LorentzRSSpinor() [3/3]

Member Function Documentation

◆ dot() [1/2]

◆ dot() [2/2]

◆ generalCurrent()

◆ generalScalar()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ setTS1()

◆ setTS2()

◆ setTS3()

◆ setTS4()

◆ setXS1()

◆ setXS2()

◆ setXS3()

◆ setXS4()

◆ setYS1()

◆ setYS2()

◆ setYS3()

◆ setYS4()

◆ setZS1()

◆ setZS2()

◆ setZS3()

◆ setZS4()

◆ ts1()

◆ ts2()

◆ ts3()

◆ ts4()

◆ Type()

◆ xs1()

◆ xs2()

◆ xs3()

◆ xs4()

◆ ys1()

◆ ys2()

◆ ys3()

◆ ys4()

◆ zs1()

◆ zs2()

◆ zs3()

◆ zs4()

Member Data Documentation

◆ _spin

◆ _type