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108 lines
3.7 KiB
Python
108 lines
3.7 KiB
Python
import warnings
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import numpy as np
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from .linalg import inv, matmul
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from .dirac import gamma, gamma5
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L = None
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T = None
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class Npr_matrix(np.ndarray):
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def __new__(cls, input_array, mom_in=None, mom_out=None):
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obj = np.asarray(input_array).view(cls)
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obj.mom_in = mom_in
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obj.mom_out = mom_out
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return obj
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@property
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def g5H(self):
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"""Gamma_5 hermitean conjugate
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Returns gamma_5 @ M.T.conj() @ gamma_5 and exchanges in and out going
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momenta. Works only for 12x12 matrices.
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"""
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if self.shape != (12, 12):
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raise Exception('g5H only works for 12x12 matrices.')
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extended_g5 = np.kron(np.eye(3, dtype=int), gamma5)
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return Npr_matrix(matmul(extended_g5, self.conj().T, extended_g5),
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mom_in=self.mom_out,
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mom_out=self.mom_in)
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def _propagate_mom(self, other, name):
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s_mom = getattr(self, name, None)
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o_mom = getattr(other, name, None)
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if s_mom is not None and o_mom is not None:
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if not np.allclose(s_mom, o_mom):
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raise Exception(name + ' does not match.')
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return o_mom if o_mom is not None else s_mom
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def __matmul__(self, other):
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return self.__new__(Npr_matrix,
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super().__matmul__(other),
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self._propagate_mom(other, 'mom_in'),
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self._propagate_mom(other, 'mom_out'))
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def __array_finalize__(self, obj):
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if obj is None:
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return
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self.mom_in = getattr(obj, 'mom_in', None)
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self.mom_out = getattr(obj, 'mom_out', None)
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def _check_geometry():
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if L is None:
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raise Exception("Spatial extent 'L' not set.")
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else:
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if not isinstance(L, int):
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raise Exception("Spatial extent 'L' must be an integer.")
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if T is None:
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raise Exception("Temporal extent 'T' not set.")
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if not isinstance(T, int):
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raise Exception("Temporal extent 'T' must be an integer.")
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def inv_propagator(prop):
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""" Inverts a 12x12 quark propagator"""
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if prop.shape != (12, 12):
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raise Exception("Only 12x12 propagators can be inverted.")
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return Npr_matrix(inv(prop), prop.mom_in)
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def Zq(inv_prop, fermion='Wilson'):
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""" Calculates the quark field renormalization constant Zq
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Parameters
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----------
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inv_prop : array
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Inverted 12x12 quark propagator
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fermion : str
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Fermion type for which the tree-level propagator is used
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in the calculation of Zq. Default Wilson.
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"""
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_check_geometry()
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mom = np.copy(inv_prop.mom_in)
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mom[3] /= T / L
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sin_mom = np.sin(2 * np.pi / L * mom)
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if fermion == 'Wilson':
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p_slash = -1j * (sin_mom[0] * gamma[0] + sin_mom[1] * gamma[1] + sin_mom[2] * gamma[2] + sin_mom[3] * gamma[3]) / np.sum(sin_mom ** 2)
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elif fermion == 'Continuum':
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p_mom = 2 * np.pi / L * mom
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p_slash = -1j * (p_mom[0] * gamma[0] + p_mom[1] * gamma[1] + p_mom[2] * gamma[2] + p_mom[3] * gamma[3]) / np.sum(p_mom ** 2)
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elif fermion == 'DWF':
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W = np.sum(1 - np.cos(2 * np.pi / L * mom))
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s2 = np.sum(sin_mom ** 2)
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p_slash = -1j * (sin_mom[0] * gamma[0] + sin_mom[1] * gamma[1] + sin_mom[2] * gamma[2] + sin_mom[3] * gamma[3])
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p_slash /= 2 * (W - 1 + np.sqrt((1 - W) ** 2 + s2))
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else:
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raise Exception("Fermion type '" + fermion + "' not implemented")
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res = 1 / 12. * np.trace(matmul(inv_prop, np.kron(np.eye(3, dtype=int), p_slash)))
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res.gamma_method()
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if not res.imag.is_zero_within_error(5):
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warnings.warn("Imaginary part of Zq is not zero within 5 sigma")
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return res
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return res.real
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