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conservation_rules

Deprecated since version 0.7.3: Use QRules and AmpForm instead

import expertsystem.reaction.conservation_rules

Collection of quantum number conservation rules for particle reactions.

This module is the place where the ‘expert’ defines the rules that verify quantum numbers of the reaction.

A rule is a function that takes quantum numbers as input and outputs a boolean. There are three different types of rules:

1. GraphElementRule that work on individual graph edges or nodes.

2. EdgeQNConservationRule that work on the interaction level, which use ingoing edges, outgoing edges as arguments. E.g.: ChargeConservation.

3. ConservationRule that work on the interaction level, which use ingoing edges, outgoing edges and a interaction node as arguments. E.g: parity_conservation.

The arguments can be any type of quantum number. However a rule argument resembling edges only accepts EdgeQuantumNumbers. Similarly arguments that resemble a node only accept NodeQuantumNumbers. The argument types do not have to be limited to a single quantum number, but can be a composite (see CParityEdgeInput).

Warning

Besides the rule logic itself, a rule also has the responsibility of stating its run conditions. These run conditions must be stated by the type annotations of its __call__ method. The type annotations therefore are not just there for static type checking: they also carry more information about the rule that is extracted dynamically by the reaction module.

Generally, the conditions can be separated into two categories:

• variable conditions

• toplogical conditions

Currently, only variable conditions are being used. Topological conditions could be created in the form of Tuple instead of List.

For additive quantum numbers, the decorator additive_quantum_number_rule can be used to automatically generate the appropriate behavior.

The module is therefore strongly typed (both for the reader of the code and for type checking with mypy). An example is HelicityParityEdgeInput, which has been defined to provide type checks on parity_conservation_helicity.

class BaryonNumberConservation(*args, **kwargs)

Bases: expertsystem.reaction.conservation_rules.EdgeQNConservationRule

Decorated via additive_quantum_number_rule.

Check for baryon_number conservation.

__call__(ingoing_edge_qns: List[baryon_number], outgoing_edge_qns: List[baryon_number]) → bool

Call self as a function.

class BottomnessConservation(*args, **kwargs)

Bases: expertsystem.reaction.conservation_rules.EdgeQNConservationRule

Decorated via additive_quantum_number_rule.

Check for bottomness conservation.

__call__(ingoing_edge_qns: List[bottomness], outgoing_edge_qns: List[bottomness]) → bool

Call self as a function.

class CParityEdgeInput(spin_magnitude, pid, c_parity=None)

Bases: object

__eq__(other)

Method generated by attrs for class CParityEdgeInput.

c_parity: Optional[c_parity]

pid: pid

spin_magnitude: spin_magnitude

class CParityNodeInput(l_magnitude, s_magnitude)

Bases: object

__eq__(other)

Method generated by attrs for class CParityNodeInput.

l_magnitude: l_magnitude

s_magnitude: s_magnitude

class ChargeConservation(*args, **kwargs)

Bases: expertsystem.reaction.conservation_rules.EdgeQNConservationRule

Decorated via additive_quantum_number_rule.

Check for charge conservation.

__call__(ingoing_edge_qns: List[charge], outgoing_edge_qns: List[charge]) → bool

Call self as a function.

class CharmConservation(*args, **kwargs)

Bases: expertsystem.reaction.conservation_rules.EdgeQNConservationRule

Decorated via additive_quantum_number_rule.

Check for charmness conservation.

__call__(ingoing_edge_qns: List[charmness], outgoing_edge_qns: List[charmness]) → bool

Call self as a function.

class ConservationRule(*args, **kwargs)

Bases: Protocol

__call__(_ConservationRule__ingoing_edge_qns: List[Any], _ConservationRule__outgoing_edge_qns: List[Any], _ConservationRule__node_qns: Any) → bool

Call self as a function.

class EdgeQNConservationRule(*args, **kwargs)

Bases: Protocol

__call__(_EdgeQNConservationRule__ingoing_edge_qns: List[Any], _EdgeQNConservationRule__outgoing_edge_qns: List[Any]) → bool

Call self as a function.

class ElectronLNConservation(*args, **kwargs)

Bases: expertsystem.reaction.conservation_rules.EdgeQNConservationRule

Decorated via additive_quantum_number_rule.

Check for electron_lepton_number conservation.

__call__(ingoing_edge_qns: List[electron_lepton_number], outgoing_edge_qns: List[electron_lepton_number]) → bool

Call self as a function.

class GParityEdgeInput(isospin_magnitude, spin_magnitude, pid, g_parity=None)

Bases: object

__eq__(other)

Method generated by attrs for class GParityEdgeInput.

g_parity: Optional[g_parity]

isospin_magnitude: isospin_magnitude

pid: pid

spin_magnitude: spin_magnitude

class GParityNodeInput(l_magnitude, s_magnitude)

Bases: object

__eq__(other)

Method generated by attrs for class GParityNodeInput.

l_magnitude: l_magnitude

s_magnitude: s_magnitude

class GellMannNishijimaInput(charge, isospin_projection=None, strangeness=None, charmness=None, bottomness=None, topness=None, baryon_number=None, electron_lepton_number=None, muon_lepton_number=None, tau_lepton_number=None)

Bases: object

__eq__(other)

Method generated by attrs for class GellMannNishijimaInput.

baryon_number: Optional[baryon_number]

bottomness: Optional[bottomness]

charge: charge

charmness: Optional[charmness]

electron_lepton_number: Optional[electron_lepton_number]

isospin_projection: Optional[isospin_projection]

muon_lepton_number: Optional[muon_lepton_number]

strangeness: Optional[strangeness]

tau_lepton_number: Optional[tau_lepton_number]

topness: Optional[topness]

class GraphElementRule(*args, **kwargs)

Bases: Protocol

__call__(_GraphElementRule__qns: Any) → bool

Call self as a function.

class HelicityParityEdgeInput(parity, spin_magnitude, spin_projection)

Bases: object

__eq__(other)

Method generated by attrs for class HelicityParityEdgeInput.

parity: parity

spin_magnitude: spin_magnitude

spin_projection: spin_projection

class IdenticalParticleSymmetryOutEdgeInput(spin_magnitude, spin_projection, pid)

Bases: object

__eq__(other)

Method generated by attrs for class IdenticalParticleSymmetryOutEdgeInput.

pid: pid

spin_magnitude: spin_magnitude

spin_projection: spin_projection

class IsoSpinEdgeInput(isospin_magnitude, isospin_projection)

Bases: object

__eq__(other)

Method generated by attrs for class IsoSpinEdgeInput.

isospin_magnitude: isospin_magnitude

isospin_projection: isospin_projection

class MassConservation(width_factor: float)

Bases: object

Mass conservation rule.

__call__(ingoing_edge_qns: List[MassEdgeInput], outgoing_edge_qns: List[MassEdgeInput]) → bool

Implements mass conservation.

\(M_{out} - N \cdot W_{out} < M_{in} + N \cdot W_{in}\)

It makes sure that the net mass outgoing state \(M_{out}\) is smaller than the net mass of the ingoing state \(M_{in}\). Also the width \(W\) of the states is taken into account.

class MassEdgeInput(mass, width=None)

Bases: object

__eq__(other)

Method generated by attrs for class MassEdgeInput.

mass: mass

width: Optional[width]

class MuonLNConservation(*args, **kwargs)

Bases: expertsystem.reaction.conservation_rules.EdgeQNConservationRule

Decorated via additive_quantum_number_rule.

Check for muon_lepton_number conservation.

__call__(ingoing_edge_qns: List[muon_lepton_number], outgoing_edge_qns: List[muon_lepton_number]) → bool

Call self as a function.

class SpinEdgeInput(spin_magnitude, spin_projection)

Bases: object

__eq__(other)

Method generated by attrs for class SpinEdgeInput.

spin_magnitude: spin_magnitude

spin_projection: spin_projection

class SpinMagnitudeNodeInput(l_magnitude, s_magnitude)

Bases: object

__eq__(other)

Method generated by attrs for class SpinMagnitudeNodeInput.

l_magnitude: l_magnitude

s_magnitude: s_magnitude

class SpinNodeInput(l_magnitude, l_projection, s_magnitude, s_projection)

Bases: object

__eq__(other)

Method generated by attrs for class SpinNodeInput.

l_magnitude: l_magnitude

l_projection: l_projection

s_magnitude: s_magnitude

s_projection: s_projection

class StrangenessConservation(*args, **kwargs)

Bases: expertsystem.reaction.conservation_rules.EdgeQNConservationRule

Decorated via additive_quantum_number_rule.

Check for strangeness conservation.

__call__(ingoing_edge_qns: List[strangeness], outgoing_edge_qns: List[strangeness]) → bool

Call self as a function.

class TauLNConservation(*args, **kwargs)

Bases: expertsystem.reaction.conservation_rules.EdgeQNConservationRule

Decorated via additive_quantum_number_rule.

Check for tau_lepton_number conservation.

__call__(ingoing_edge_qns: List[tau_lepton_number], outgoing_edge_qns: List[tau_lepton_number]) → bool

Call self as a function.

additive_quantum_number_rule(quantum_number: type) → Callable[[Any], EdgeQNConservationRule]

Class decorator for creating an additive conservation rule.

Use this decorator to create a EdgeQNConservationRule for a quantum number to which an additive conservation rule applies:

\[\sum q_{in} = \sum q_{out}\]

Parameters

quantum_number – Quantum number to which you want to apply the additive conservation check. An example would be EdgeQuantumNumbers.charge.

c_parity_conservation(ingoing_edge_qns: List[CParityEdgeInput], outgoing_edge_qns: List[CParityEdgeInput], interaction_node_qns: CParityNodeInput) → bool

Check for \(C\)-parity conservation.

Implements \(C_{in} = C_{out}\).

clebsch_gordan_helicity_to_canonical(ingoing_spins: List[SpinEdgeInput], outgoing_spins: List[SpinEdgeInput], interaction_qns: SpinNodeInput) → bool

Implement Clebsch-Gordan checks.

For \(S_1, S_2\) to \(S\) and the \(L,S\) to \(J\) coupling based on the conversion of helicity to canonical amplitude sums.

Note

This rule does not check that the spin magnitudes couple correctly to L and S, as this is already performed by spin_magnitude_conservation.

g_parity_conservation(ingoing_edge_qns: List[GParityEdgeInput], outgoing_edge_qns: List[GParityEdgeInput], interaction_qns: GParityNodeInput) → bool

Check for \(G\)-parity conservation.

Implements for \(G_{in} = G_{out}\).

gellmann_nishijima(edge_qns: GellMannNishijimaInput) → bool

Check the Gell-Mann–Nishijima formula.

Gell-Mann–Nishijima formula:

\[Q = I_3 + \frac{1}{2}(B+S+C+B'+T)\]

where \(Q\) is charge (computed), \(I_3\) is Spin.projection of isospin, \(B\) is baryon_number, \(S\) is strangeness, \(C\) is charmness, \(B'\) is bottomness, and \(T\) is topness.

helicity_conservation(ingoing_spin_mags: List[spin_magnitude], outgoing_helicities: List[spin_projection]) → bool

Implementation of helicity conservation.

Check for \(|\lambda_2-\lambda_3| \leq S_1\).

identical_particle_symmetrization(ingoing_parities: List[parity], outgoing_edge_qns: List[IdenticalParticleSymmetryOutEdgeInput]) → bool

Verifies multi particle state symmetrization for identical particles.

In case of a multi particle state with identical particles, their exchange symmetry has to follow the spin statistic theorem.

For bosonic systems the total exchange symmetry (parity) has to be even (+1). For fermionic systems the total exchange symmetry (parity) has to be odd (-1).

In case of a particle decaying into N identical particles (N>1), the decaying particle has to have the same parity as required by the spin statistic theorem of the multi body state.

isospin_conservation(ingoing_isospins: List[IsoSpinEdgeInput], outgoing_isospins: List[IsoSpinEdgeInput]) → bool

Check for isospin conservation.

Implements

\[|I_1 - I_2| \leq I \leq |I_1 + I_2|\]

Also checks \(I_{1,z} + I_{2,z} = I_z\) and if Clebsch-Gordan coefficients are all 0.

isospin_validity(isospin: IsoSpinEdgeInput) → bool

Check for valid isospin magnitude and projection.

ls_spin_validity(spin_input: SpinNodeInput) → bool

Check for valid isospin magnitude and projection.

parity_conservation(ingoing_edge_qns: List[parity], outgoing_edge_qns: List[parity], l_magnitude: l_magnitude) → bool

Implement \(P_{in} = P_{out} \cdot (-1)^L\).

parity_conservation_helicity(ingoing_edge_qns: List[HelicityParityEdgeInput], outgoing_edge_qns: List[HelicityParityEdgeInput], parity_prefactor: parity_prefactor) → bool

Implements parity conservation for helicity formalism.

Check the following:

\[A_{-\lambda_1-\lambda_2} = P_1 P_2 P_3 (-1)^{S_2+S_3-S_1} A_{\lambda_1\lambda_2}\]

\[\mathrm{parity\,prefactor} = P_1 P_2 P_3 (-1)^{S_2+S_3-S_1}\]

Note

Only the special case \(\lambda_1=\lambda_2=0\) may return False independent on the parity prefactor.

spin_conservation(ingoing_spins: List[SpinEdgeInput], outgoing_spins: List[SpinEdgeInput], interaction_qns: SpinNodeInput) → bool

Check for spin conservation.

Implements

\[|S_1 - S_2| \leq S \leq |S_1 + S_2|\]

and

\[|L - S| \leq J \leq |L + S|\]

Also checks \(M_1 + M_2 = M\) and if Clebsch-Gordan coefficients are all 0.

spin_magnitude_conservation(ingoing_spins: List[SpinEdgeInput], outgoing_spins: List[SpinEdgeInput], interaction_qns: SpinMagnitudeNodeInput) → bool

Check for spin conservation.

Implements

\[|S_1 - S_2| \leq S \leq |S_1 + S_2|\]

and

\[|L - S| \leq J \leq |L + S|\]

spin_validity(spin: SpinEdgeInput) → bool

Check for valid spin magnitude and projection.

combinatorics default_settings