Implement vertex operators #40545
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Implement vertex operators #40545
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Vertex operators
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Documentation preview for this PR (built with commit 44039aa; changes) is ready! 🎉 |
tscrim
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Sep 8, 2025
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I will probably have more on my second pass, but this is coming together.
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| lazy_import('sage.algebras.yangian', 'Yangian') | ||
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| import sage.algebras.vertex_operators_catalog as vertex_operators |
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| import sage.algebras.vertex_operators_catalog as vertex_operators | |
| lazy_import("sage.algebras", "vertex_operators_catalog", "vertex_operators") |
so it is not imported at startup.
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| from sage.misc.lazy_import import lazy_import | ||
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| lazy_import('sage.algebras.vertex_operators', 'BosonicFockSpace') | ||
| lazy_import('sage.algebras.vertex_operators', 'CreationOperator') | ||
| lazy_import('sage.algebras.vertex_operators', 'AnnihilationOperator') | ||
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| del lazy_import # We remove the object from here so it doesn't appear under tab completion |
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| from sage.misc.lazy_import import lazy_import | |
| lazy_import('sage.algebras.vertex_operators', 'BosonicFockSpace') | |
| lazy_import('sage.algebras.vertex_operators', 'CreationOperator') | |
| lazy_import('sage.algebras.vertex_operators', 'AnnihilationOperator') | |
| del lazy_import # We remove the object from here so it doesn't appear under tab completion | |
| from sage.algebras.vertex_operators import (BosonicFockSpace, CreationOperator, AnnihilationOperator) |
If we lazily import the catalog, then we don't have to lazily import here.
| from sage.structure.unique_representation import UniqueRepresentation | ||
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| class FermionicFockSpace(CombinatorialFreeModule): |
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This class can be replaced by
Ind = cartesian_product((Partitions(), ZZ))
CombinatorialFreeModule(R, Ind, bracket=['|', '>'])| if isinstance(sym_basis, str): | ||
| b = getattr(Sym, sym_basis, None) | ||
| if b is None or b() not in Sym.realizations(): | ||
| raise ValueError("Unknown symmetric function basis") |
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| raise ValueError("Unknown symmetric function basis") | |
| raise ValueError("unknown symmetric function basis") |
We follow Python's conventions.
| raise ValueError("Unknown symmetric function basis") | ||
| return LaurentPolynomialRing(b(), names=(name,)) | ||
| if sym_basis.base_ring() is not R: | ||
| raise ValueError("") |
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| self.pos = HalfVertexOperator(pos) | ||
| self.neg = HalfVertexOperator(neg) | ||
| if fockspace is None: | ||
| fockspace = BosonicFockSpace() | ||
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| self.cutoff = cutoff | ||
| self.dcharge = dcharge |
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| self.pos = HalfVertexOperator(pos) | |
| self.neg = HalfVertexOperator(neg) | |
| if fockspace is None: | |
| fockspace = BosonicFockSpace() | |
| self.cutoff = cutoff | |
| self.dcharge = dcharge | |
| self._pos = HalfVertexOperator(pos) | |
| self._neg = HalfVertexOperator(neg) | |
| if fockspace is None: | |
| fockspace = BosonicFockSpace() | |
| self._cutoff = cutoff | |
| self._dcharge = dcharge |
| bra[1], self.fockspace.zero()).monomial_coefficients().get(Partition(bra[0]), self.fockspace.zero())) | ||
| return F if cutoff is None else self._approximate(F, cutoff) | ||
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| def _approximate(self, family, cutoff): |
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This should not be a method of this class but a function.
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| # op is a scalar | ||
| if op in R.base_ring(): | ||
| return op*f |
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| return op*f | |
| return op * f |
PEP8
| raise ValueError | ||
| for i in range(len(mon) - 1, -1, -1): | ||
| x = self.vertex_ops[i].act_on(mon[i], x) | ||
| if x == 0: |
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| if x == 0: | |
| if not x: |
| res[m] = c | ||
| return res | ||
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| def vacuum_expectation(self, cutoff=None): |
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Good to move up to the base class.
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This PR adds classes which implement the vertex operators relating to the classical boson-fermion correspondence.
Part of #40241
cc: @tscrim
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