ThePEG::LorentzRotation Class Reference

The LorentzRotation class combine a SpinOneLorentzRotation and a spin SpinHalfLorentzRotation to provide members which can perform the Lorentz transformation of any object. More...

#include <LorentzRotation.h>

List of all members.

Public Member Functions

bool isIdentity () const

Returns true if the Identity matrix.

LorentzRotation inverse () const

Return the inverse.

LorentzRotation & invert ()

Inverts the LorentzRotation matrix.

std::ostream & print (std::ostream &os) const

output operator

Constructors and destructor.

LorentzRotation ()

Default constructor.

LorentzRotation (double bx, double by, double bz, double gamma=-1.)

Constructor giving the components of a Lorentz boost.

LorentzRotation (const Boost &b, double gamma=-1.)

Constructor giving the vector for a Lorentz boost.

Set methods for speical cases of simple rotations and boosts

LorentzRotation & setBoost (double bx, double by, double bz, double gamma=-1.)

Specify the components of a Lorentz Boost.

LorentzRotation & setBoost (const Boost &b, double gamma=-1.)

Specify a Lorentz Boost as a vector.

LorentzRotation & setBoostX (double boost)

Specify a boost by the given factor along the x-axis.

LorentzRotation & setBoostY (double boost)

Specify a boost by the given factor along the y-axis.

LorentzRotation & setBoostZ (double boost)

Specify a boost by the given factor along the z-axis.

LorentzRotation & setRotate (double delta, const Axis &axis)

Specify a rotation about a general axis by the angle given.

LorentzRotation & setRotateX (double angle)

Specify a rotation by the given angle about the x-axis.

LorentzRotation & setRotateY (double angle)

Specify a rotation by the given angle about the y-axis.

LorentzRotation & setRotateZ (double angle)

Specify a rotation by the given angle about the z-axis.

Methods to return the spin-\f$\frac12\f$ and spin-1 transformations

const SpinHalfLorentzRotation & half () const

The spin- $\frac12$ transformation.

const SpinOneLorentzRotation & one () const

The spin-1 transformation.

operator const SpinOneLorentzRotation & () const

Automatically cast to the spin-1 transformation.

Access methods for the components of the spin-1 rotation

double xx () const

The xx component.

double xy () const

The xy component.

double xz () const

The xz component.

double xt () const

The xt component.

double yx () const

The yx component.

double yy () const

The yy component.

double yz () const

The yz component.

double yt () const

The yt component.

double zx () const

The zx component.

double zy () const

The zy component.

double zz () const

The zz component.

double zt () const

The zt component.

double tx () const

The tx component.

double ty () const

The ty component.

double tz () const

The tz component.

double tt () const

The tt component.

Access methods for the components of the spin-\f$\frac12\f$ rotation

Complex s1s1 () const

The $(1,1)$ component.

Complex s1s2 () const

The $(1,2)$ component.

Complex s1s3 () const

The $(1,3)$ component.

Complex s1s4 () const

The $(1,4)$ component.

Complex s2s1 () const

The $(1,1)$ component.

Complex s2s2 () const

The $(1,1)$ component.

Complex s2s3 () const

The $(1,1)$ component.

Complex s2s4 () const

The $(1,1)$ component.

Complex s3s1 () const

The $(1,1)$ component.

Complex s3s2 () const

The $(1,1)$ component.

Complex s3s3 () const

The $(1,1)$ component.

Complex s3s4 () const

The $(1,1)$ component.

Complex s4s1 () const

The $(1,1)$ component.

Complex s4s2 () const

The $(1,1)$ component.

Complex s4s3 () const

The $(1,1)$ component.

Complex s4s4 () const

The $(1,1)$ component.

Transformation and product members

template<typename Value>

LorentzVector< Value > operator* (const LorentzVector< Value > &lv) const

Product with a LorentzVector simply returns the rotated vector.

template<typename Value>

Lorentz5Vector< Value > operator* (const Lorentz5Vector< Value > &lv) const

Product with a Lorentz5Vector simply returns the rotated vector.

LorentzRotation operator* (const LorentzRotation &lt) const

Product of two LorentzRotations (this) * lt - matrix multiplication.

LorentzRotation & operator*= (const LorentzRotation &lt)

Multiply by and assign a*=b becomes a= a*b.

LorentzRotation & transform (const LorentzRotation &lt)

Transform (similar to *= but a.transform(b) becomes a = b*a.

LorentzRotation & rotateX (double delta)

Rotation around the x-axis; equivalent to LT = RotationX(delta) * LT.

LorentzRotation & rotateY (double delta)

Rotation around the y-axis; equivalent to LT = RotationY(delta) * LT.

LorentzRotation & rotateZ (double delta)

Rotation around the z-axis; equivalent to LT = RotationZ(delta) * LT.

LorentzRotation & rotate (double delta, const Axis &axis)

Rotation around specified vector - LT = Rotation(delta,axis)*LT.

LorentzRotation & boostX (double beta)

Pure boost along the x-axis; equivalent to LT = BoostX(beta) * LT.

LorentzRotation & boostY (double beta)

Pure boost along the y-axis; equivalent to LT = BoostX(beta) * LT.

LorentzRotation & boostZ (double beta)

Pure boost along the z-axis; equivalent to LT = BoostX(beta) * LT.

LorentzRotation & boost (double bx, double by, double bz, double gamma=-1.)

boost equivalent to LT = Boost(bx,by,bz) * LT

LorentzRotation & boost (const Boost &bv, double gamma=-1.)

boost equivalent to LT = Boost(bv) * LT

Private Attributes

SpinHalfLorentzRotation _half

The spin- $\frac12$ rotation.

SpinOneLorentzRotation _one

The spin-1 rotation.

Friends

LorentzRotation inverseOf (const LorentzRotation &lt)

The external inverseOf needs to be a friend.

Detailed Description

The LorentzRotation class combine a SpinOneLorentzRotation and a spin SpinHalfLorentzRotation to provide members which can perform the Lorentz transformation of any object.

The class ensures that the two transformations are consistent by only allowing transformations to be made to both the spin-1 and spin- $\frac12$ members.

Definition at line 27 of file LorentzRotation.h.

Constructor & Destructor Documentation

ThePEG::LorentzRotation::LorentzRotation ( ) [inline]

Default constructor.

Gives a unit matrix.

Definition at line 42 of file LorentzRotation.h.

ThePEG::LorentzRotation::LorentzRotation	(	double	bx,
		double	by,
		double	bz,
		double	gamma = `-1.`
	)			`[inline]`

Constructor giving the components of a Lorentz boost.

Parameters:

	bx	The x-component of the boost
	by	The y-component of the boost
	bz	The z-component of the boost
	gamma	The $\gamma$ factor (optional)

Definition at line 51 of file LorentzRotation.h.

ThePEG::LorentzRotation::LorentzRotation	(	const Boost &	b,
		double	gamma = `-1.`
	)			`[inline]`

Constructor giving the vector for a Lorentz boost.

Parameters:

	b	The boost vector
	gamma	The $\gamma$ factor (optional)

Definition at line 59 of file LorentzRotation.h.

Member Function Documentation

LorentzRotation& ThePEG::LorentzRotation::setBoost	(	double	bx,
		double	by,
		double	bz,
		double	gamma = `-1.`
	)			`[inline]`

Specify the components of a Lorentz Boost.

Parameters:

	bx	The x-component of the boost
	by	The y-component of the boost
	bz	The z-component of the boost
	gamma	The $\gamma$ factor (optional)

Definition at line 102 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::setBoost(), and ThePEG::SpinHalfLorentzRotation::setBoost().

LorentzRotation& ThePEG::LorentzRotation::setBoost	(	const Boost &	b,
		double	gamma = `-1.`
	)			`[inline]`

Specify a Lorentz Boost as a vector.

Parameters:

	b	The boost vector
	gamma	The $\gamma$ factor (optional)

Definition at line 113 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::setBoost(), and ThePEG::SpinHalfLorentzRotation::setBoost().

LorentzRotation& ThePEG::LorentzRotation::setBoostX ( double boost ) [inline]

Specify a boost by the given factor along the x-axis.

Parameters:

boost

The Lorentz boost

Definition at line 123 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::setBoost(), and ThePEG::SpinHalfLorentzRotation::setBoostX().

LorentzRotation& ThePEG::LorentzRotation::setBoostY ( double boost ) [inline]

Specify a boost by the given factor along the y-axis.

Parameters:

boost

The Lorentz boost

Definition at line 133 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::setBoost(), and ThePEG::SpinHalfLorentzRotation::setBoostY().

LorentzRotation& ThePEG::LorentzRotation::setBoostZ ( double boost ) [inline]

Specify a boost by the given factor along the z-axis.

Parameters:

boost

The Lorentz boost

Definition at line 143 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::setBoost(), and ThePEG::SpinHalfLorentzRotation::setBoostZ().

LorentzRotation& ThePEG::LorentzRotation::setRotate	(	double	delta,
		const Axis &	axis
	)			`[inline]`

Specify a rotation about a general axis by the angle given.

Parameters:

	delta	The angle
	axis	The axis

Definition at line 154 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::setRotate(), and ThePEG::SpinHalfLorentzRotation::setRotate().

LorentzRotation& ThePEG::LorentzRotation::setRotateX ( double angle ) [inline]

Specify a rotation by the given angle about the x-axis.

Parameters:

angle

The rotation angle

Definition at line 164 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::setRotateX(), and ThePEG::SpinHalfLorentzRotation::setRotateX().

LorentzRotation& ThePEG::LorentzRotation::setRotateY ( double angle ) [inline]

Specify a rotation by the given angle about the y-axis.

Parameters:

angle

The rotation angle

Definition at line 174 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::setRotateZ(), and ThePEG::SpinHalfLorentzRotation::setRotateZ().

LorentzRotation& ThePEG::LorentzRotation::setRotateZ ( double angle ) [inline]

Specify a rotation by the given angle about the z-axis.

Parameters:

angle

The rotation angle

Definition at line 184 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::setRotateZ(), and ThePEG::SpinHalfLorentzRotation::setRotateZ().

LorentzRotation ThePEG::LorentzRotation::operator* ( const LorentzRotation & lt ) const [inline]

Product of two LorentzRotations (this) * lt - matrix multiplication.

Parameters:

lt

The LorentzRotation we are multiplying

Definition at line 399 of file LorentzRotation.h.

References _half, and _one.

LorentzRotation& ThePEG::LorentzRotation::boost	(	double	bx,
		double	by,
		double	bz,
		double	gamma = `-1.`
	)			`[inline]`

boost equivalent to LT = Boost(bx,by,bz) * LT

Parameters:

	bx	The x-component of the boost
	by	The y-component of the boost
	bz	The z-component of the boost
	gamma	The $\gamma$ factor (optional)

Definition at line 494 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::boost(), and ThePEG::SpinHalfLorentzRotation::boost().

LorentzRotation& ThePEG::LorentzRotation::boost	(	const Boost &	bv,
		double	gamma = `-1.`
	)			`[inline]`

boost equivalent to LT = Boost(bv) * LT

Parameters:

	bv	The boost
	gamma	The $\gamma$ factor (optional)

Definition at line 505 of file LorentzRotation.h.

References _half, _one, ThePEG::SpinOneLorentzRotation::boost(), and ThePEG::SpinHalfLorentzRotation::boost().

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

LorentzRotation.h


Public Member Functions
bool	isIdentity () const
	Returns true if the Identity matrix.
LorentzRotation	inverse () const
	Return the inverse.
LorentzRotation &	invert ()
	Inverts the LorentzRotation matrix.
std::ostream &	print (std::ostream &os) const
	output operator
Constructors and destructor.
	LorentzRotation ()
	Default constructor.
	LorentzRotation (double bx, double by, double bz, double gamma=-1.)
	Constructor giving the components of a Lorentz boost.
	LorentzRotation (const Boost &b, double gamma=-1.)
	Constructor giving the vector for a Lorentz boost.
Set methods for speical cases of simple rotations and boosts
LorentzRotation &	setBoost (double bx, double by, double bz, double gamma=-1.)
	Specify the components of a Lorentz Boost.
LorentzRotation &	setBoost (const Boost &b, double gamma=-1.)
	Specify a Lorentz Boost as a vector.
LorentzRotation &	setBoostX (double boost)
	Specify a boost by the given factor along the x-axis.
LorentzRotation &	setBoostY (double boost)
	Specify a boost by the given factor along the y-axis.
LorentzRotation &	setBoostZ (double boost)
	Specify a boost by the given factor along the z-axis.
LorentzRotation &	setRotate (double delta, const Axis &axis)
	Specify a rotation about a general axis by the angle given.
LorentzRotation &	setRotateX (double angle)
	Specify a rotation by the given angle about the x-axis.
LorentzRotation &	setRotateY (double angle)
	Specify a rotation by the given angle about the y-axis.
LorentzRotation &	setRotateZ (double angle)
	Specify a rotation by the given angle about the z-axis.
Methods to return the spin-\f$\frac12\f$ and spin-1 transformations
const SpinHalfLorentzRotation &	half () const
	The spin- $\frac12$ transformation.
const SpinOneLorentzRotation &	one () const
	The spin-1 transformation.
	operator const SpinOneLorentzRotation & () const
	Automatically cast to the spin-1 transformation.
Access methods for the components of the spin-1 rotation
double	xx () const
	The xx component.
double	xy () const
	The xy component.
double	xz () const
	The xz component.
double	xt () const
	The xt component.
double	yx () const
	The yx component.
double	yy () const
	The yy component.
double	yz () const
	The yz component.
double	yt () const
	The yt component.
double	zx () const
	The zx component.
double	zy () const
	The zy component.
double	zz () const
	The zz component.
double	zt () const
	The zt component.
double	tx () const
	The tx component.
double	ty () const
	The ty component.
double	tz () const
	The tz component.
double	tt () const
	The tt component.
Access methods for the components of the spin-\f$\frac12\f$ rotation
Complex	s1s1 () const
	The component.
Complex	s1s2 () const
	The component.
Complex	s1s3 () const
	The component.
Complex	s1s4 () const
	The component.
Complex	s2s1 () const
	The component.
Complex	s2s2 () const
	The component.
Complex	s2s3 () const
	The component.
Complex	s2s4 () const
	The component.
Complex	s3s1 () const
	The component.
Complex	s3s2 () const
	The component.
Complex	s3s3 () const
	The component.
Complex	s3s4 () const
	The component.
Complex	s4s1 () const
	The component.
Complex	s4s2 () const
	The component.
Complex	s4s3 () const
	The component.
Complex	s4s4 () const
	The component.
Transformation and product members
template<typename Value>
LorentzVector< Value >	operator* (const LorentzVector< Value > &lv) const
	Product with a LorentzVector simply returns the rotated vector.
template<typename Value>
Lorentz5Vector< Value >	operator* (const Lorentz5Vector< Value > &lv) const
	Product with a Lorentz5Vector simply returns the rotated vector.
LorentzRotation	operator* (const LorentzRotation &lt) const
	Product of two LorentzRotations (this) * lt - matrix multiplication.
LorentzRotation &	operator*= (const LorentzRotation &lt)
	Multiply by and assign a=b becomes a= ab.
LorentzRotation &	transform (const LorentzRotation &lt)
	Transform (similar to = but a.transform(b) becomes a = ba.
LorentzRotation &	rotateX (double delta)
	Rotation around the x-axis; equivalent to LT = RotationX(delta) * LT.
LorentzRotation &	rotateY (double delta)
	Rotation around the y-axis; equivalent to LT = RotationY(delta) * LT.
LorentzRotation &	rotateZ (double delta)
	Rotation around the z-axis; equivalent to LT = RotationZ(delta) * LT.
LorentzRotation &	rotate (double delta, const Axis &axis)
	Rotation around specified vector - LT = Rotation(delta,axis)*LT.
LorentzRotation &	boostX (double beta)
	Pure boost along the x-axis; equivalent to LT = BoostX(beta) * LT.
LorentzRotation &	boostY (double beta)
	Pure boost along the y-axis; equivalent to LT = BoostX(beta) * LT.
LorentzRotation &	boostZ (double beta)
	Pure boost along the z-axis; equivalent to LT = BoostX(beta) * LT.
LorentzRotation &	boost (double bx, double by, double bz, double gamma=-1.)
	boost equivalent to LT = Boost(bx,by,bz) * LT
LorentzRotation &	boost (const Boost &bv, double gamma=-1.)
	boost equivalent to LT = Boost(bv) * LT
Private Attributes
SpinHalfLorentzRotation	_half
	The spin- $\frac12$ rotation.
SpinOneLorentzRotation	_one
	The spin-1 rotation.
Friends
LorentzRotation	inverseOf (const LorentzRotation &lt)
	The external inverseOf needs to be a friend.