lips.particle
- class lips.particle.Particle(kinematics=None, real_momentum=False, field=Field('mpc', 0, 300))
Describes the kinematics of a single particle.
- angles_for_squares()
Flips left and right spinors.
- comp_twist_x(other)
x^{˙αα} = (μⱼ^{˙α} λᵢ^α - μᵢ^{˙α} λⱼ^α ) / ⟨ij⟩
- property four_mom
Four Momentum with upper index: P^μ
- property four_mom_d
Four Momentum with lower index: P_μ
- property is_lightlike
- property is_massless
- property l_sp_d
Left spinor with index down: λ̅_α̇ (row vector).
- property l_sp_u
Left spinor with index up: λ̅^α̇ (column vector).
- lsq()
Lorentz dot product with itself: 2 trace(P^{α̇α}P̅̅_{αα̇}) = P^μ * η_μν * P^ν.
- property m
- property m2
- property r2_sp
Four Momentum Slashed with upper indices: P^{α̇α}
- property r2_sp_b
Four Momentum Slashed with lower indices: P̅̅_{αα̇}
- property r_sp_d
Right spinor with index down: λ_α (column vector).
- property r_sp_u
Right spinor with index up: λ^α (row vector).
- randomise(real_momentum=False)
- randomise_mpc(real_momentum=False)
Randomises its momentum.
- randomise_spinors_in_field()
- randomise_twist()
- property spin_index
- property spinors_are_in_field_extension
- to_field(field)
- twist_x_to_mom(other)
lips.particles
- class lips.particles.Particles(number_of_particles_or_particles=None, seed=None, real_momenta=False, field=Field('mpc', 0, 300), fix_mom_cons=True, internal_masses=None)
Describes the kinematics of n particles. Base one list of Particle objects.
- analytical_subs_d()
- angles_for_squares()
Switches all angle brackets for square brackets and viceversa.
- static check_consistency(temp_string)
- cluster(llIntegers, massive_fermions=None, massive_spins=())
Returns clustered particle objects according to lists of lists of integers (e.g. corners of one loop diagram). Also useful to build phase space configurations with external massive legs. Massive legs are by default massive scalars. Massive fermions can be specificed as e.g.: massive_fermions=((3, ‘u’, all), (4, ‘d’, all))) More generally, massive spin can be specified as: massive_spins=((index, (left position, left value), (right position, right value)), )
- copy()
Return a shallow copy of the list.
- fix_mom_cons(A=0, B=0, real_momenta=False, axis=1)
Fixes momentum conservation using particles A and B.
- four_momenta_for_mathematica(as_spinors=False)
- ijk_to_3Ks(ijk)
- ijk_to_3NonOverlappingLists(ijk, mode=1)
- image(permutation_or_rule)
Returns the image of self under a given permutation or rule. Remember, this is a passive transformation.
- insert(index, *args)
Insert object before index.
- property internal_masses_dict
- property m2s
Masses squared of all particles in phase space.
- make_analytical_d(indepVars=None, symbols=('a', 'b', 'c', 'd'))
- momentum_conservation_check(silent=True)
Returns true if momentum is conserved.
- property ms
Masses of all particles in phase space.
- property multiplicity
- onshell_relation_check(silent=True)
Returns true if all on-shell relations are satisfied.
- phasespace_consistency_check(invariants=[], silent=True)
Runs momentum and onshell checks. Looks for outliers in phase space. Returns: mom_cons, on_shell, big_outliers, small_outliers.
- randomise_all(real_momenta=False)
Randomises all particles. Breaks momentum conservation.
- randomise_twistor()
- save_phase_space_point(invariant='')
- property spinors_are_in_field_extension
- subs(myDict)
Substitutes symbols with values from myDict, acts depending on whether the particle is massless or not.
- swap_spin_indices_positions()
- to_field(field)
- property total_mom
Total momentum of the given phase space as a rank two spinor.
- class lips.particles_compute.Particles_Compute
- compute(original_temp_string)
Computes spinor strings.
Available variables: ⟨a|b⟩, [a|b], ⟨a|b+c|d], ⟨a|b+c|d+e|f], …, s_ijk, Δ_ijk, Ω_ijk, Π_ijk, tr5_ijkl
- ee(i, j)
Contraction of two polarization tensors. Requires .helconf property to be set.
- ep(i, j)
Contraction of polarization tensor with four momentum. Requires .helconf property to be set.
- ldot(A, B)
Lorentz dot product: 1/2 trace(P^{α̇α}P̅̅_{αα̇}) = P_A^μ * η_μν * P_B^ν.
- pe(i, j)
Contraction of four momentum with polarization tensor. Requires .helconf property to be set.
- lips.particles_compute.as_scalar_if_scalar(func)
Turns numpy arrays with zero dimensions into ‘real’ scalars.
lips.particles_set
- class lips.hardcoded_limits.particles_set.Particles_Set
lips.particles_set_pair
- class lips.hardcoded_limits.particles_set_pair.Particles_SetPair
Module contents
Defines tools for phase space manipulations. Particles objects are base one lists of Particle objects.
Particles objects allow to:
Compute spinor strings, through .compute;
Construct single collinear limits, through .set;
Construct double collinear limits, through .set_pair.
1oParticles = Particles(multiplicity)
2oParticles.randomise_all()
3oParticles.fix_mom_cons()
4oParticles.compute(spinor_string)
5oParticles.set(spinor_string, small_value)
6oParticles.set_pair(spinor_string_1, small_value_1, spinor_string_2, small_value_2)
- class lips.Invariants(n, no_cached=False, no_hard_coded_ones=False, Restrict3Brackets=True, Restrict4Brackets=True, FurtherRestrict4Brackets=True, verbose=False)
- GenerateFromScratch(n, no_hard_coded_ones=False, Restrict3Brackets=True, Restrict4Brackets=True, FurtherRestrict4Brackets=True)
- property full
- property full_minus_4_brackets
- property invs_N
- property pw_cache
- property pw_invariants
- class lips.Particle(kinematics=None, real_momentum=False, field=Field('mpc', 0, 300))
Describes the kinematics of a single particle.
- angles_for_squares()
Flips left and right spinors.
- comp_twist_x(other)
x^{˙αα} = (μⱼ^{˙α} λᵢ^α - μᵢ^{˙α} λⱼ^α ) / ⟨ij⟩
- property four_mom
Four Momentum with upper index: P^μ
- property four_mom_d
Four Momentum with lower index: P_μ
- property is_lightlike
- property is_massless
- property l_sp_d
Left spinor with index down: λ̅_α̇ (row vector).
- property l_sp_u
Left spinor with index up: λ̅^α̇ (column vector).
- lsq()
Lorentz dot product with itself: 2 trace(P^{α̇α}P̅̅_{αα̇}) = P^μ * η_μν * P^ν.
- property m
- property m2
- property r2_sp
Four Momentum Slashed with upper indices: P^{α̇α}
- property r2_sp_b
Four Momentum Slashed with lower indices: P̅̅_{αα̇}
- property r_sp_d
Right spinor with index down: λ_α (column vector).
- property r_sp_u
Right spinor with index up: λ^α (row vector).
- randomise(real_momentum=False)
- randomise_mpc(real_momentum=False)
Randomises its momentum.
- randomise_spinors_in_field()
- randomise_twist()
- property spin_index
- property spinors_are_in_field_extension
- to_field(field)
- twist_x_to_mom(other)
- class lips.Particles(number_of_particles_or_particles=None, seed=None, real_momenta=False, field=Field('mpc', 0, 300), fix_mom_cons=True, internal_masses=None)
Describes the kinematics of n particles. Base one list of Particle objects.
- analytical_subs_d()
- angles_for_squares()
Switches all angle brackets for square brackets and viceversa.
- static check_consistency(temp_string)
- cluster(llIntegers, massive_fermions=None, massive_spins=())
Returns clustered particle objects according to lists of lists of integers (e.g. corners of one loop diagram). Also useful to build phase space configurations with external massive legs. Massive legs are by default massive scalars. Massive fermions can be specificed as e.g.: massive_fermions=((3, ‘u’, all), (4, ‘d’, all))) More generally, massive spin can be specified as: massive_spins=((index, (left position, left value), (right position, right value)), )
- copy()
Return a shallow copy of the list.
- fix_mom_cons(A=0, B=0, real_momenta=False, axis=1)
Fixes momentum conservation using particles A and B.
- four_momenta_for_mathematica(as_spinors=False)
- ijk_to_3Ks(ijk)
- ijk_to_3NonOverlappingLists(ijk, mode=1)
- image(permutation_or_rule)
Returns the image of self under a given permutation or rule. Remember, this is a passive transformation.
- insert(index, *args)
Insert object before index.
- property internal_masses_dict
- property m2s
Masses squared of all particles in phase space.
- make_analytical_d(indepVars=None, symbols=('a', 'b', 'c', 'd'))
- momentum_conservation_check(silent=True)
Returns true if momentum is conserved.
- property ms
Masses of all particles in phase space.
- property multiplicity
- onshell_relation_check(silent=True)
Returns true if all on-shell relations are satisfied.
- phasespace_consistency_check(invariants=[], silent=True)
Runs momentum and onshell checks. Looks for outliers in phase space. Returns: mom_cons, on_shell, big_outliers, small_outliers.
- randomise_all(real_momenta=False)
Randomises all particles. Breaks momentum conservation.
- randomise_twistor()
- save_phase_space_point(invariant='')
- property spinors_are_in_field_extension
- subs(myDict)
Substitutes symbols with values from myDict, acts depending on whether the particle is massless or not.
- swap_spin_indices_positions()
- to_field(field)
- property total_mom
Total momentum of the given phase space as a rank two spinor.
- lips.ldot(oP1, oP2)
- exception lips.myException