NAME
Physics::Lorentz::Transformation - Representation of Poincare Transformations
SYNOPSIS
use Physics::Lorentz;
my $rotation = Physics::Lorentz::Transformation->rotation_euler(
$alpha, $beta, $gamma
);
my $vector = Physics::Lorentz::Vector->new([$t, $x, $y, $z]);
my $rotated = $rotation->apply($vector);
# or: $rotated = $rotation * $vector;
...DESCRIPTION
This class represents a Poincare transformation. That is a proper or improper Lorentz transformation plus a shift by some 4-vector. (x' = lamda*x + a)
Yes, the class name might be misleading, but honestly, when most non-physicists talk about Lorentz transformations, they mean Poincare transformations anyway. (Pun intended.)
To sum this up, the set of Poincare transformations contains, among others
Boosts
Rotations
Space Inversions / Parity
Time Inversion
Shifts by a constant vector
Combinations thereof
EXPORT
None.
OVERLOADED INTERFACE
Stringification is overloaded with the stringify method.
Multiplication (*) is overloaded with the merge method for other transformations: $t3 = $t1 * $t2 corresponds to the following application on a vector: t1 * ( t2 * vec ). (I.e. t2 first, then t1) Of course, Poincare transformations do not commute!
The assignment form of multiplication is supported for merging transformations but its use is discouraged unless you're into obfuscation.
Multiplication is also overloaded for application to vectors, but only if the vector is on the right of the transformation: $t * $v is okay, but $v * $t is not.
CONSTRUCTORS
new
Creates a new Physics::Lorentz::Transformation object. Defaults to the unity transformation.
If one argument is present, this argument may either be a 4x4 PDL which will be used internally as the PDL representation of the or an equivalent Perl datastructure (4x4 matrix).
If two arguments are present, the second argument will be used as or converted to a Physics::Lorentz::Vector. It defaults to [0, 0, 0, 0]
This result will be of the form x' = lamda * x + a where lamda is the matrix and a is the vector. (And x is the 4-vector that's acted upon.)
rotation_euler
Alternative constructor to construct a specific type of Lorentz transformation: A 3D rotation with the Euler angles alpha, beta, gamma.
Three arguments: alpha, beta, gamma.
(First rotate about fixed z-axis by alpha, the about fixed y-axis about beta, then about fixed z-axis by gamma.)
rotation_x
Alternative constructor to construct a specific type of Lorentz transformation: A 3D rotation about the x or 1-axis. First argument is the rotation angle.
rotation_y
Alternative constructor to construct a specific type of Lorentz transformation: A 3D rotation about the y or 2-axis. First argument is the rotation angle.
rotation_z
Alternative constructor to construct a specific type of Lorentz transformation: A 3D rotation about the z or 3-axis. First argument is the rotation angle.
boost
Alternative constructor to construct a specific type of Lorentz transformation: A boost of rapidity eta (eta = atanh(v/c)) and direction x.
Accepts three arguments: The components of the boost's velocity vector divided by the speed of light: (v1/c, v2/c, v3/c).
boost_x
Alternative constructor to construct a specific type of Lorentz transformation: A boost of rapidity eta (eta = atanh(v/c)) parallel to the x axis.
Accepts one argument: The boost's velocity divided by the speed of light v/c.
boost_y
Alternative constructor to construct a specific type of Lorentz transformation: A boost of rapidity eta (eta = atanh(v/c)) parallel to the y axis.
Accepts one argument: The boost's velocity divided by the speed of light v/c.
boost_z
Alternative constructor to construct a specific type of Lorentz transformation: A boost of rapidity eta (eta = atanh(v/c)) parallel to the z axis.
Accepts one argument: The boost's velocity divided by the speed of light v/c.
parity
Returns the parity operation, that is, space inversion.
time_reversal
Returns the time reversal operation.
OTHER METHODS
merge
Merge two transformations into one. Mathematically speaking, if a is the current transformation, b is another, and v is a Lorentz vector, $a->merge($b) is the transformation v' = a x (b x v). In words, if applied to a vector, the merged transformation is the subsequent application of tranformation b and then a.
apply
Apply transformation to a Lorentz vector or something that can be converted into a Physics::Lorentz::Vector. Returns a vector.
clone
Returns a copy of the object.
stringify
Returns a string representation of the object. Currently, this is the string representation of the internal PDL vector/matrix.
ACCESSORS
get_matrix
Returns the 4x4 PDL that represents the Lorentz transformation.
This is the actual object that is used inside the Transformation object, so be aware that modifying it results in action at a distance!
get_vector
Returns the Physics::Lorentz::Vector object that is used inside the Transformation object. As with the matrix, this is the actual object. Same caveats.
Note that this isn't a PDL but a Physics::Lorentz::Vector object.
SEE ALSO
PDL, Physics::Lorentz, Physics::Lorentz::Vector,
AUTHOR
Steffen Müller, <smueller@cpan.org>
COPYRIGHT AND LICENSE
Copyright (C) 2006 by Steffen Müller
This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.6 or, at your option, any later version of Perl 5 you may have available.
1 POD Error
The following errors were encountered while parsing the POD:
- Around line 639:
Non-ASCII character seen before =encoding in 'Müller,'. Assuming UTF-8