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Class TempLat::FieldFunctionals

ClassList > TempLat > FieldFunctionals

A class which stores expressions of field functionals. By "field functional" we refer to any function of the field variables such as quadratic forms, e.g. <phi^2>, and others. More...

  • #include <fieldfunctionals.h>

Public Functions

Type Name
FieldFunctionals () = delete

Public Static Functions

Type Name
auto B2SU2 (Model & model, Tag< A > a)
Returns the square of the field strength tensor of the SU2 gauge field, i.e. <F_{ij}^2> (sum over i,j). This is equivalent to the square of the magnetic field, and we compute it from the plaquette.
auto B2U1 (Model & model, Tag< A > a)
Returns the square of the field strength tensor of the U1 gauge field, i.e. <F_{ij}^2> (sum over i,j).
auto EBU1 (Model & model, Tag< N > n)
Returns the product of E and B fields for the U1 gauge field, which gives the topological charge density.
auto TrEBSU2 (Model & model, Tag< N > n)
Returns the product of E and B fields for the SU2 gauge field, which gives the topological charge density.
auto get_SU2_electric (Model & model, Tag< N > n, Tag< DIR > i)
Returns "momentum" of the SU(2) gauge fields' EOM (a bit different because evolving the links). Also note that our algebra variables are antihermitean, so we are really saving i E.
auto get_SU2_electric (Model & model, Tag< N > n)
Returns the electric field for the SU2 gauge field, as a vector with the components in each spatial direction.
auto grad2CS (Model & model, Tag< I > i)
Returns the square of the covariant gradient of the complex scalar field, i.e. <D_i[f]^2> (sum over i). Note that for a complex scalar, the covariant derivative includes the gauge field.
auto grad2S (Model & model, Tag< I > i)
Returns the square of the gradient of the scalar field, i.e. <D_i[f]^2> (sum over i). Note that for a scalar singlet, the covariant derivative reduces to the ordinary gradient, so we can use the norm of the gradient squared directly.
auto grad2SU2Doublet (Model & model, Tag< I > i)
Returns the square of the covariant gradient of the SU2 doublet field, i.e. <D_i[f]^2> (sum over i). Note that for a SU2 doublet, the covariant derivative includes the gauge field.
auto pi2CS (Model & model, Tag< I > i)
Returns the square of the canonical momentum of the complex scalar field, i.e. <pi^2>.
auto pi2S (Model & model, Tag< I > i)
Returns the square of the canonical momentum of the scalar field, i.e. <pi^2>.
auto pi2SU2 (Model & model, Tag< A > a)
This is a bit of a misnommer. We return the quantity that is related to the eletric field by powers of a(t).
auto pi2SU2Doublet (Model & model, Tag< I > i)
Returns the square of the canonical momentum of the SU2 doublet field, i.e. <pi^2>.
auto pi2U1 (Model & model, Tag< A > a)
Returns the square of the canonical momentum of the U1 gauge field, i.e. <pi^2>.

Detailed Description

The methods of this class compute the field functionals that appear in the total energy density, but without the corresponding multiplying factors. For example, when we compute <Pi^2> for a scalar singlet, only in energies.h we multiply it by 1/2*a^(-6) to get the corresponding kinetic energy.

Public Functions Documentation

function FieldFunctionals

TempLat::FieldFunctionals::FieldFunctionals () = delete

Public Static Functions Documentation

function B2SU2

Returns the square of the field strength tensor of the SU2 gauge field, i.e. <F_{ij}^2> (sum over i,j). This is equivalent to the square of the magnetic field, and we compute it from the plaquette. 

template<class Model, int A>
static inline auto TempLat::FieldFunctionals::B2SU2 (
    Model & model,
    Tag < A > a
)

Parameters:

  • model The model from which to extract the field.
  • a The tag corresponding to the SU2 gauge field in the model.

function B2U1

Returns the square of the field strength tensor of the U1 gauge field, i.e. <F_{ij}^2> (sum over i,j). 

template<class Model, int A>
static inline auto TempLat::FieldFunctionals::B2U1 (
    Model & model,
    Tag < A > a
)

Parameters:

  • model The model from which to extract the field.
  • a The tag corresponding to the U1 gauge field in the model.

function EBU1

Returns the product of E and B fields for the U1 gauge field, which gives the topological charge density. 

template<class Model, int N>
static inline auto TempLat::FieldFunctionals::EBU1 (
    Model & model,
    Tag < N > n
)

Parameters:

  • model The model from which to extract the field.
  • n The tag corresponding to the U1 gauge field in the model

function TrEBSU2

Returns the product of E and B fields for the SU2 gauge field, which gives the topological charge density. 

template<class Model, int N>
static inline auto TempLat::FieldFunctionals::TrEBSU2 (
    Model & model,
    Tag < N > n
)

Parameters:

  • model The model from which to extract the field.
  • n The tag corresponding to the SU2 gauge field in the model

function get_SU2_electric [1/2]

Returns "momentum" of the SU(2) gauge fields' EOM (a bit different because evolving the links). Also note that our algebra variables are antihermitean, so we are really saving i E. 

template<class Model, int N, int DIR>
static inline auto TempLat::FieldFunctionals::get_SU2_electric (
    Model & model,
    Tag < N > n,
    Tag < DIR > i
)

Parameters:

  • model The model from which to extract the field.
  • n The tag corresponding to the SU2 gauge field in the model.
  • i The tag corresponding to the spatial direction.

function get_SU2_electric [2/2]

Returns the electric field for the SU2 gauge field, as a vector with the components in each spatial direction. 

template<class Model, int N>
static inline auto TempLat::FieldFunctionals::get_SU2_electric (
    Model & model,
    Tag < N > n
)

Parameters:

  • model The model from which to extract the field.
  • n The tag corresponding to the SU2 gauge field.

function grad2CS

Returns the square of the covariant gradient of the complex scalar field, i.e. <D_i[f]^2> (sum over i). Note that for a complex scalar, the covariant derivative includes the gauge field. 

template<class Model, int I>
static inline auto TempLat::FieldFunctionals::grad2CS (
    Model & model,
    Tag < I > i
)

Uses the forward covariant gradient.

Parameters:

  • model The model from which to extract the field and the gauge field.
  • i The tag corresponding to the complex scalar field in the model.

function grad2S

Returns the square of the gradient of the scalar field, i.e. <D_i[f]^2> (sum over i). Note that for a scalar singlet, the covariant derivative reduces to the ordinary gradient, so we can use the norm of the gradient squared directly. 

template<class Model, int I>
static inline auto TempLat::FieldFunctionals::grad2S (
    Model & model,
    Tag < I > i
)

Parameters:

  • model The model from which to extract the field.
  • i The tag corresponding to the scalar field in the model.

function grad2SU2Doublet

Returns the square of the covariant gradient of the SU2 doublet field, i.e. <D_i[f]^2> (sum over i). Note that for a SU2 doublet, the covariant derivative includes the gauge field. 

template<class Model, int I>
static inline auto TempLat::FieldFunctionals::grad2SU2Doublet (
    Model & model,
    Tag < I > i
)

Parameters:

  • model The model from which to extract the field and the gauge field.
  • i The tag corresponding to the SU2 doublet field in the model.

function pi2CS

Returns the square of the canonical momentum of the complex scalar field, i.e. <pi^2>. 

template<class Model, int I>
static inline auto TempLat::FieldFunctionals::pi2CS (
    Model & model,
    Tag < I > i
)

Parameters:

  • model The model from which to extract the field.
  • i The tag corresponding to the complex scalar field in the model.

function pi2S

Returns the square of the canonical momentum of the scalar field, i.e. <pi^2>. 

template<class Model, int I>
static inline auto TempLat::FieldFunctionals::pi2S (
    Model & model,
    Tag < I > i
)

Parameters:

  • model The model from which to extract the field.
  • i The tag corresponding to the scalar field in the model.

function pi2SU2

This is a bit of a misnommer. We return the quantity that is related to the eletric field by powers of a(t). 

template<class Model, int A>
static inline auto TempLat::FieldFunctionals::pi2SU2 (
    Model & model,
    Tag < A > a
)

Parameters:

  • model The model from which to extract the field.
  • a The tag corresponding to the SU2 gauge field in the model.

function pi2SU2Doublet

Returns the square of the canonical momentum of the SU2 doublet field, i.e. <pi^2>. 

template<class Model, int I>
static inline auto TempLat::FieldFunctionals::pi2SU2Doublet (
    Model & model,
    Tag < I > i
)

Parameters:

  • model The model from which to extract the field.
  • i The tag corresponding to the SU2 doublet field in the model.

function pi2U1

Returns the square of the canonical momentum of the U1 gauge field, i.e. <pi^2>. 

template<class Model, int A>
static inline auto TempLat::FieldFunctionals::pi2U1 (
    Model & model,
    Tag < A > a
)

Parameters:

  • model The model from which to extract the field.
  • a The tag corresponding to the U1 gauge field in the model.

The documentation for this class was generated from the following file cosmolatticeweb/tmp/code_source/cosmolattice/include/CosmoInterface/definitions/fieldfunctionals.h