actions – SPHINCS

This submodule contains the implementations of the actions of the TYPES representing the members of the Lorentz group defined in MODULE lorentz_group, presently boosts and spatial rotations, to geometrical objects

FT 08.12.2022

Uses

- Ancestors:
- lorentz_group
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Module Procedures

apply_as_congruence_to_symrank2_tensor apply_as_congruence_to_tensor apply_as_similarity_to_symrank2_tensor apply_as_similarity_to_tensor apply_to_vector

Module Procedures

module procedure apply_as_congruence_to_symrank2_tensor module function apply_as_congruence_to_symrank2_tensor(this, t) result(transformed_t)

Implements the action of a boost as a similarity on a $10$ -vector storing the components of a symmetric $4\times 4$ tensor

Arguments

Type	Intent	Optional	Attributes		Name
class(lorentz_transformation),	intent(in)			::	this	lorentz_transformation object to apply
double precision,	intent(in),		DIMENSION(n_sym4x4)	::	t	$10$ -vector storing the components of the symmetric $4\times 4$ tensor to be boosted

Return Value double precision, DIMENSION(n_sym4x4)

$10$ -vector storing the components of the boosted symmetric $4\times 4$ tensor

module procedure apply_as_congruence_to_tensor module function apply_as_congruence_to_tensor(this, t) result(transformed_t)

Implements the action of a boost as a congruence on a metric

Arguments

Type	Intent	Optional	Attributes		Name
class(lorentz_transformation),	intent(in)			::	this	lorentz_transformation object to apply
double precision,	intent(in),		DIMENSION(4,4)	::	t(0:3,0:3)	$4\times 4$ tensor to be boosted

Return Value double precision, DIMENSION(4,4), (0:3,0:3)

Boosted $4\times 4$ tensor

module procedure apply_as_similarity_to_symrank2_tensor module function apply_as_similarity_to_symrank2_tensor(this, t) result(transformed_t)

Implements the action of a boost as a similarity on a $10$ -vector storing the components of a symmetric $4\times 4$ tensor

Arguments

Type	Intent	Optional	Attributes		Name
class(lorentz_transformation),	intent(in)			::	this	lorentz_transformation object to apply
double precision,	intent(in),		DIMENSION(n_sym4x4)	::	t	$10$ -vector storing the components of the symmetric $4\times 4$ tensor to be boosted

Return Value double precision, DIMENSION(n_sym4x4)

$10$ -vector storing the components of the boosted symmetric $4\times 4$ tensor

module procedure apply_as_similarity_to_tensor module function apply_as_similarity_to_tensor(this, t) result(transformed_t)

Implements the action of a boost as a similarity on a linear operator

Arguments

Type	Intent	Optional	Attributes		Name
class(lorentz_transformation),	intent(in)			::	this	lorentz_transformation object to apply
double precision,	intent(in),		DIMENSION(4,4)	::	t(0:3,0:3)	$4\times 4$ tensor to be boosted

Return Value double precision, DIMENSION(4,4), (0:3,0:3)

Boosted $4\times 4$ tensor

module procedure apply_to_vector module function apply_to_vector(this, u) result(transformed_u)

Implements the action of a boost on a $4-$ vector

Arguments

Type	Intent	Optional	Attributes		Name
class(lorentz_transformation),	intent(in)			::	this	lorentz_transformation object to apply
double precision,	intent(in),		DIMENSION(4)	::	u(0:3)	$4$ -vector to be boosted

Return Value double precision, DIMENSION(4), (0:3)

Boosted $4$ -vector

actions Submodule

Contents

Module Procedures

Uses

Ancestors:

Contents

Module Procedures

Module Procedures

module procedure apply_as_congruence_to_symrank2_tensor module function apply_as_congruence_to_symrank2_tensor(this, t) result(transformed_t)

Arguments

Return Value double precision, DIMENSION(n_sym4x4)

module procedure apply_as_congruence_to_tensor module function apply_as_congruence_to_tensor(this, t) result(transformed_t)

Arguments

Return Value double precision, DIMENSION(4,4), (0:3,0:3)

module procedure apply_as_similarity_to_symrank2_tensor module function apply_as_similarity_to_symrank2_tensor(this, t) result(transformed_t)

Arguments

Return Value double precision, DIMENSION(n_sym4x4)

module procedure apply_as_similarity_to_tensor module function apply_as_similarity_to_tensor(this, t) result(transformed_t)

Arguments

Return Value double precision, DIMENSION(4,4), (0:3,0:3)

module procedure apply_to_vector module function apply_to_vector(this, u) result(transformed_u)

Arguments

Return Value double precision, DIMENSION(4), (0:3)

actions Submodule

Contents

Module Procedures

Uses

Ancestors:

Contents

Module Procedures

Module Procedures

module procedure apply_as_congruence_to_symrank2_tensor module function apply_as_congruence_to_symrank2_tensor(this, t) result(transformed_t) Interface →

Arguments

Return Value double precision, DIMENSION(n_sym4x4)

module procedure apply_as_congruence_to_tensor module function apply_as_congruence_to_tensor(this, t) result(transformed_t) Interface →

Arguments

Return Value double precision, DIMENSION(4,4), (0:3,0:3)

module procedure apply_as_similarity_to_symrank2_tensor module function apply_as_similarity_to_symrank2_tensor(this, t) result(transformed_t) Interface →

Arguments

Return Value double precision, DIMENSION(n_sym4x4)

module procedure apply_as_similarity_to_tensor module function apply_as_similarity_to_tensor(this, t) result(transformed_t) Interface →

Arguments

Return Value double precision, DIMENSION(4,4), (0:3,0:3)

module procedure apply_to_vector module function apply_to_vector(this, u) result(transformed_u) Interface →

Arguments

Return Value double precision, DIMENSION(4), (0:3)

module procedure apply_as_congruence_to_symrank2_tensor module function apply_as_congruence_to_symrank2_tensor(this, t) result(transformed_t)

module procedure apply_as_congruence_to_tensor module function apply_as_congruence_to_tensor(this, t) result(transformed_t)

module procedure apply_as_similarity_to_symrank2_tensor module function apply_as_similarity_to_symrank2_tensor(this, t) result(transformed_t)

module procedure apply_as_similarity_to_tensor module function apply_as_similarity_to_tensor(this, t) result(transformed_t)

module procedure apply_to_vector module function apply_to_vector(this, u) result(transformed_u)