ROOT::Math::Boost Class Reference

Lorentz boost class with the (4D) transformation represented internally by a 4x4 orthosymplectic matrix.

A variable names bgamma appears in several places in this file.

See also BoostX, BoostY and BoostZ for classes representing specialized Lorentz boosts. Also, the 3-D rotation classes can be considered to be special Lorentz transformations which do not mix space and time components.

See also

Overview of the physics vector library

A few words of elaboration are needed to make its meaning clear. On page 69 of Misner, Thorne and Wheeler, (Exercise 2.7) the elements of the matrix for a general Lorentz boost are given as

$${\mathrm{\Lambda }}_k^{j^{\prime }}={\mathrm{\Lambda }}_j^{k^{\prime }}=(\gamma -1)n^j{n}^k+{\delta }^{jk}$$

where the n^i are unit vectors in the direction of the three spatial axes. Using the definitions, $n^i={\beta }_i/\beta$ , then, for example,

$${\mathrm{\Lambda }}_{xy}=(\gamma -1)n_x{n}_y=(\gamma -1){\beta }_x{\beta }_y/{\beta }^2$$

By definition,

$${\gamma }^2=1/(1-{\beta }^2)$$

so that

$${\gamma }^2{\beta }^2={\gamma }^2-1$$

or

$${\beta }^2=({\gamma }^2-1)/{\gamma }^2$$

If we insert this into the expression for ${\mathrm{\Lambda }}_{xy}$, we get

$${\mathrm{\Lambda }}_{xy}=(\gamma -1){\gamma }^2/({\gamma }^2-1){\beta }_x{\beta }_y$$

or, finally

$${\mathrm{\Lambda }}_{xy}={\gamma }^2/(\gamma +1){\beta }_x{\beta }_y$$

The expression ${\gamma }^2/(\gamma +1)$ is what we call bgamma in the code below.

Definition at line 47 of file Boost.h.

Public Types
enum	EBoostMatrixIndex {   kXX = 0 , kXY = 1 , kXZ = 2 , kXT = 3 ,   kYY = 4 , kYZ = 5 , kYT = 6 , kZZ = 7 ,   kZT = 8 , kTT = 9 }
enum	ELorentzRotationMatrixIndex {   kLXX = 0 , kLXY = 1 , kLXZ = 2 , kLXT = 3 ,   kLYX = 4 , kLYY = 5 , kLYZ = 6 , kLYT = 7 ,   kLZX = 8 , kLZY = 9 , kLZZ = 10 , kLZT = 11 ,   kLTX = 12 , kLTY = 13 , kLTZ = 14 , kLTT = 15 }
typedef double	Scalar
typedef DisplacementVector3D< Cartesian3D< double >, DefaultCoordinateSystemTag >	XYZVector
	The beta vector for this boost.

Public Member Functions
	Boost ()
	Default constructor (identity transformation)
	Boost (Boost const &b)
	copy constructor
	Boost (BoostX const &bx)
	Construct from an axial boost.
	Boost (BoostY const &by)
	Boost (BoostZ const &bz)
template<class Avector >
	Boost (const Avector &beta)
	Construct given a beta vector (which must have methods x(), y(), z())
template<class IT >
	Boost (IT begin, IT end)
	Construct given a pair of pointers or iterators defining the beginning and end of an array of three Scalars to use as beta_x, _y, and _z.
	Boost (Scalar beta_x, Scalar beta_y, Scalar beta_z)
	Construct given a three Scalars beta_x, beta_y, and beta_z.
XYZVector	BetaVector () const
template<class IT >
void	GetComponents (IT begin) const
	Get given a pointer or an iterator defining the beginning of an array into which to place beta_x, beta_y, and beta_z.
template<class IT >
void	GetComponents (IT begin, IT end) const
	Get given a pair of pointers or iterators defining the beginning and end of an array of three Scalars into which to place beta_x, beta_y, and beta_z.
void	GetComponents (Scalar &beta_x, Scalar &beta_y, Scalar &beta_z) const
	Get components into beta_x, beta_y, and beta_z.
void	GetLorentzRotation (Scalar r[]) const
	Get elements of internal 4x4 symmetric representation, into a data array suitable for direct use as the components of a LorentzRotation Note – 16 Scalars will be written into the array; if the array is not that large, then this will lead to undefined behavior.
Boost	Inverse () const
	Return inverse of a boost.
void	Invert ()
	Invert a Boost in place.
bool	operator!= (const Boost &rhs) const
template<class Foreign4Vector >
Foreign4Vector	operator() (const Foreign4Vector &v) const
	Lorentz transformation operation on an arbitrary 4-vector v.
template<class CoordSystem >
LorentzVector< CoordSystem >	operator() (const LorentzVector< CoordSystem > &v) const
	Lorentz transformation operation on a LorentzVector in any coordinate system.
LorentzVector< ROOT::Math::PxPyPzE4D< double > >	operator() (const LorentzVector< ROOT::Math::PxPyPzE4D< double > > &v) const
	Lorentz transformation operation on a Minkowski ('Cartesian') LorentzVector.
template<class A4Vector >
A4Vector	operator* (const A4Vector &v) const
	Overload operator * for boost on a vector.
Boost &	operator= (Boost const &rhs)
	Assignment operator.
Boost &	operator= (BoostX const &bx)
	Assign from an axial pure boost.
Boost &	operator= (BoostY const &by)
Boost &	operator= (BoostZ const &bz)
bool	operator== (const Boost &rhs) const
	Equality/inequality operators.
void	Rectify ()
	Re-adjust components to eliminate small deviations from a perfect orthosyplectic matrix.
template<class Avector >
void	SetComponents (const Avector &beta)
	Set components from a beta vector.
template<class IT >
void	SetComponents (IT begin, IT end)
	Set given a pair of pointers or iterators defining the beginning and end of an array of three Scalars to use as beta_x,beta _y, and beta_z.
void	SetComponents (Scalar beta_x, Scalar beta_y, Scalar beta_z)
	Set components from beta_x, beta_y, and beta_z.

Protected Member Functions
void	SetIdentity ()

Private Attributes
Scalar	fM [10]

#include <Math/GenVector/Boost.h>

Member Typedef Documentation

Scalar

typedef double ROOT::Math::Boost::Scalar

Definition at line 51 of file Boost.h.

XYZVector

typedef DisplacementVector3D<Cartesian3D<double>, DefaultCoordinateSystemTag > ROOT::Math::Boost::XYZVector

The beta vector for this boost.

Definition at line 200 of file Boost.h.

Member Enumeration Documentation

EBoostMatrixIndex

enum ROOT::Math::Boost::EBoostMatrixIndex

Enumerator
kXX
kXY
kXZ
kXT
kYY
kYZ
kYT
kZZ
kZT
kTT

Definition at line 60 of file Boost.h.

ELorentzRotationMatrixIndex

enum ROOT::Math::Boost::ELorentzRotationMatrixIndex

Enumerator
kLXX
kLXY
kLXZ
kLXT
kLYX
kLYY
kLYZ
kLYT
kLZX
kLZY
kLZZ
kLZT
kLTX
kLTY
kLTZ
kLTT

Definition at line 53 of file Boost.h.

Constructor & Destructor Documentation

Boost() [1/8]

ROOT::Math::Boost::Boost ( )

inline

Default constructor (identity transformation)

Definition at line 72 of file Boost.h.

Boost() [2/8]

ROOT::Math::Boost::Boost ( Scalar beta_x, Scalar beta_y, Scalar beta_z )

inline

Construct given a three Scalars beta_x, beta_y, and beta_z.

Definition at line 77 of file Boost.h.

Boost() [3/8]

template<class Avector >

ROOT::Math::Boost::Boost ( const Avector & beta )

inlineexplicit

Construct given a beta vector (which must have methods x(), y(), z())

Definition at line 85 of file Boost.h.

Boost() [4/8]

template<class IT >

ROOT::Math::Boost::Boost ( IT begin, IT end )

inline

Construct given a pair of pointers or iterators defining the beginning and end of an array of three Scalars to use as beta_x, _y, and _z.

Definition at line 92 of file Boost.h.

Boost() [5/8]

ROOT::Math::Boost::Boost ( Boost const & b )

inline

copy constructor

Definition at line 97 of file Boost.h.

Boost() [6/8]

ROOT::Math::Boost::Boost ( BoostX const & bx )

inlineexplicit

Construct from an axial boost.

Definition at line 105 of file Boost.h.

Boost() [7/8]

ROOT::Math::Boost::Boost ( BoostY const & by )

inlineexplicit

Definition at line 106 of file Boost.h.

Boost() [8/8]

ROOT::Math::Boost::Boost ( BoostZ const & bz )

inlineexplicit

Definition at line 107 of file Boost.h.

Member Function Documentation

BetaVector()

DisplacementVector3D< Cartesian3D< Boost::Scalar > > ROOT::Math::Boost::BetaVector

(

)

const

Definition at line 108 of file Boost.cxx.

GetComponents() [1/3]

template<class IT >

void ROOT::Math::Boost::GetComponents ( IT begin ) const

inline

Get given a pointer or an iterator defining the beginning of an array into which to place beta_x, beta_y, and beta_z.

Definition at line 189 of file Boost.h.

GetComponents() [2/3]

template<class IT >

void ROOT::Math::Boost::GetComponents ( IT begin, IT end ) const

inline

Get given a pair of pointers or iterators defining the beginning and end of an array of three Scalars into which to place beta_x, beta_y, and beta_z.

Definition at line 177 of file Boost.h.

GetComponents() [3/3]

void ROOT::Math::Boost::GetComponents	(	Scalar &	beta_x,
		Scalar &	beta_y,
		Scalar &	beta_z ) const

Get components into beta_x, beta_y, and beta_z.

Definition at line 99 of file Boost.cxx.

GetLorentzRotation()

void ROOT::Math::Boost::GetLorentzRotation

(

Scalar

r[]

)

const

Get elements of internal 4x4 symmetric representation, into a data array suitable for direct use as the components of a LorentzRotation Note – 16 Scalars will be written into the array; if the array is not that large, then this will lead to undefined behavior.

Definition at line 115 of file Boost.cxx.

Inverse()

Boost ROOT::Math::Boost::Inverse

(

)

const

Return inverse of a boost.

Definition at line 163 of file Boost.cxx.

Invert()

void ROOT::Math::Boost::Invert

(

)

Invert a Boost in place.

Definition at line 156 of file Boost.cxx.

operator!=()

bool ROOT::Math::Boost::operator!= ( const Boost & rhs ) const

inline

Definition at line 275 of file Boost.h.

operator()() [1/3]

template<class Foreign4Vector >

Foreign4Vector ROOT::Math::Boost::operator() ( const Foreign4Vector & v ) const

inline

Lorentz transformation operation on an arbitrary 4-vector v.

Preconditions: v must implement methods x(), y(), z(), and t() and the arbitrary vector type must have a constructor taking (x,y,z,t)

Definition at line 240 of file Boost.h.

operator()() [2/3]

template<class CoordSystem >

LorentzVector< CoordSystem > ROOT::Math::Boost::operator() ( const LorentzVector< CoordSystem > & v ) const

inline

Lorentz transformation operation on a LorentzVector in any coordinate system.

Definition at line 227 of file Boost.h.

operator()() [3/3]

LorentzVector< PxPyPzE4D< double > > ROOT::Math::Boost::operator()

(

const LorentzVector< ROOT::Math::PxPyPzE4D< double > > &

v

)

const

Lorentz transformation operation on a Minkowski ('Cartesian') LorentzVector.

Definition at line 143 of file Boost.cxx.

operator*()

template<class A4Vector >

A4Vector ROOT::Math::Boost::operator* ( const A4Vector & v ) const

inline

Overload operator * for boost on a vector.

Definition at line 251 of file Boost.h.

operator=() [1/4]

Boost & ROOT::Math::Boost::operator= ( Boost const & rhs )

inline

Assignment operator.

Definition at line 115 of file Boost.h.

operator=() [2/4]

Boost & ROOT::Math::Boost::operator= ( BoostX const & bx )

inline

Assign from an axial pure boost.

Definition at line 126 of file Boost.h.

operator=() [3/4]

Boost & ROOT::Math::Boost::operator= ( BoostY const & by )

inline

Definition at line 128 of file Boost.h.

operator=() [4/4]

Boost & ROOT::Math::Boost::operator= ( BoostZ const & bz )

inline

Definition at line 130 of file Boost.h.

operator==()

bool ROOT::Math::Boost::operator== ( const Boost & rhs ) const

inline

Equality/inequality operators.

Definition at line 269 of file Boost.h.

Rectify()

void ROOT::Math::Boost::Rectify

(

)

Re-adjust components to eliminate small deviations from a perfect orthosyplectic matrix.

Definition at line 123 of file Boost.cxx.

SetComponents() [1/3]

template<class Avector >

void ROOT::Math::Boost::SetComponents ( const Avector & beta )

inline

Set components from a beta vector.

Definition at line 157 of file Boost.h.

SetComponents() [2/3]

template<class IT >

void ROOT::Math::Boost::SetComponents ( IT begin, IT end )

inline

Set given a pair of pointers or iterators defining the beginning and end of an array of three Scalars to use as beta_x,beta _y, and beta_z.

Definition at line 165 of file Boost.h.

SetComponents() [3/3]

void ROOT::Math::Boost::SetComponents	(	Scalar	beta_x,
		Scalar	beta_y,
		Scalar	beta_z )

Set components from beta_x, beta_y, and beta_z.

Definition at line 76 of file Boost.cxx.

SetIdentity()

void ROOT::Math::Boost::SetIdentity ( )

protected

Definition at line 67 of file Boost.cxx.

Member Data Documentation

fM

Scalar ROOT::Math::Boost::fM[10]

private

Definition at line 285 of file Boost.h.

Libraries for ROOT::Math::Boost:

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

• math/genvector/inc/Math/GenVector/Boost.h
• math/genvector/src/Boost.cxx