DiFfRG::fRG::TFLitimSpatial Namespace Reference

Here, useful threshold functions obtained by performing loop integrals with the litim regulator are collected. For explicit expressions, see the appendix of https://arxiv.org/abs/1909.02991. More...

Functions
template<int nb, typename NT >
NT	B (const NT &mb2, const double &k, const double &T)
template<int nf, typename NT >
NT	F (const NT &mf2, const double &k, const double &T, const double &mu)
template<int nb1, int nb2, typename NT , typename NT1 , typename NT2 >
NT	BB (const NT1 &mb12, const NT2 &mb22, const double &k, const double &T)
template<int nf, int nb, typename NT , typename NTf , typename NTb >
NT	FBFermiPiT (const NTf &mf2, const NTb &mb2, const double &k, const double &T, const double &mu)
template<unsigned lev, typename NT1 , typename NT2 >
auto	lB (const NT1 &mb2, const NT2 &etab, const double &k, const double &T, const double &d)
template<unsigned lev, typename NT >
auto	lB (const NT &mb2, const double &k, const double &T, const double &d)
template<unsigned lev, typename NT1 , typename NT2 >
auto	lF (const NT1 &mf2, const NT2 &etaf, const double &k, const double &T, const double &mu, const double &d)
template<unsigned lev, typename NT >
auto	lF (const NT &mf2, const double &k, const double &T, const double &mu, const double &d)
template<unsigned levf, unsigned levb, typename NT , typename NT1 , typename NT2 , typename NT3 , typename NT4 >
NT	LFB (const NT1 &mf2, const NT2 &mb2, const NT3 &etaf, const NT4 &etab, const double &k, const double &T, const double &mu, const double &d)
template<unsigned levf, unsigned levb, typename NT , typename NT1 , typename NT2 >
auto	LFB (const NT1 &mf2, const NT2 &mb2, const double &k, const double &T, const double &mu, const double &d)

Detailed Description

Here, useful threshold functions obtained by performing loop integrals with the litim regulator are collected. For explicit expressions, see the appendix of https://arxiv.org/abs/1909.02991.

Function Documentation

B()

template<int nb, typename NT >

NT DiFfRG::fRG::TFLitimSpatial::B	(	const NT &	mb2,
		const double &	k,
		const double &	T
	)

BB()

template<int nb1, int nb2, typename NT , typename NT1 , typename NT2 >

NT DiFfRG::fRG::TFLitimSpatial::BB	(	const NT1 &	mb12,
		const NT2 &	mb22,
		const double &	k,
		const double &	T
	)

F()

template<int nf, typename NT >

NT DiFfRG::fRG::TFLitimSpatial::F	(	const NT &	mf2,
		const double &	k,
		const double &	T,
		const double &	mu
	)

FBFermiPiT()

template<int nf, int nb, typename NT , typename NTf , typename NTb >

NT DiFfRG::fRG::TFLitimSpatial::FBFermiPiT	(	const NTf &	mf2,
		const NTb &	mb2,
		const double &	k,
		const double &	T,
		const double &	mu
	)

lB() [1/2]

template<unsigned lev, typename NT >

auto DiFfRG::fRG::TFLitimSpatial::lB	(	const NT &	mb2,
		const double &	k,
		const double &	T,
		const double &	d
	)

This is lB_nb which contains nb bosonic propagators in the loop, runs without etas for LPA.

Parameters

mb2	boson mass
mi	an instance of a model

lB() [2/2]

template<unsigned lev, typename NT1 , typename NT2 >

auto DiFfRG::fRG::TFLitimSpatial::lB	(	const NT1 &	mb2,
		const NT2 &	etab,
		const double &	k,
		const double &	T,
		const double &	d
	)

This is lB_nb which contains nb bosonic propagators in the loop.

Parameters

mb2	boson mass
etab	boson eta
mi	an instance of a model0

lF() [1/2]

template<unsigned lev, typename NT >

auto DiFfRG::fRG::TFLitimSpatial::lF	(	const NT &	mf2,
		const double &	k,
		const double &	T,
		const double &	mu,
		const double &	d
	)

This is lF_nf which contains nf fermionic propagators in the loop, runs without etas for LPA.

Parameters

mf2	fermion mass
mi	an instance of a model

lF() [2/2]

template<unsigned lev, typename NT1 , typename NT2 >

auto DiFfRG::fRG::TFLitimSpatial::lF	(	const NT1 &	mf2,
		const NT2 &	etaf,
		const double &	k,
		const double &	T,
		const double &	mu,
		const double &	d
	)

This is lF_nf which contains nf fermionic propagators in the loop.

Parameters

mf2	fermion mass
etaf	fermion eta
mi	an instance of a model

LFB() [1/2]

template<unsigned levf, unsigned levb, typename NT , typename NT1 , typename NT2 >

auto DiFfRG::fRG::TFLitimSpatial::LFB	(	const NT1 &	mf2,
		const NT2 &	mb2,
		const double &	k,
		const double &	T,
		const double &	mu,
		const double &	d
	)

This is L_nf_nb which contains nf fermionic and nb bosonic propagators in the loop, with the external (fermionic) momentum set to p = (pi T, 0); runs without etas for LPA.

Parameters

mf2	fermion mass
mb2	boson mass
mi	an instance of a model

LFB() [2/2]

template<unsigned levf, unsigned levb, typename NT , typename NT1 , typename NT2 , typename NT3 , typename NT4 >

NT DiFfRG::fRG::TFLitimSpatial::LFB	(	const NT1 &	mf2,
		const NT2 &	mb2,
		const NT3 &	etaf,
		const NT4 &	etab,
		const double &	k,
		const double &	T,
		const double &	mu,
		const double &	d
	)

This is L_nf_nb which contains nf fermionic and nb bosonic propagators in the loop, with the external (fermionic) momentum set to p = (pi T, 0).

Parameters

mf2	fermion mass
mb2	boson mass
etaf	fermion eta
etab	boson eta
mi	an instance of a model