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| - | ====== Overview of HEP features ====== | ||
| - | <html> | ||
| - | <div class="text-right" style="font-size: 15px; "> | ||
| - | </html> | ||
| - | Next topic: [[documentation:guide:mappings_of_indices]] | ||
| - | <html> | ||
| - | <span class="glyphicon glyphicon-arrow-right"></span> | ||
| - | </div> | ||
| - | </html> | ||
| - | |||
| - | ---- | ||
| - | |||
| - | |||
| - | Besides general features for manipulation with tensors and a [[list of transformations|wide range of general-purpose transformations]], Redberry provides a set of transformations and functions required for high energy physics (HEP). | ||
| - | |||
| - | ====Calculation of one-loop counterterms==== | ||
| - | Redberry provides a set of tools for calculation of one-loop counterterms in curved space-time. These tools allow to calculate one-loop counterterms of an arbitrary theory (with second or fourth order operator in Lagrangian quadratic form) and background in four dimensions in curved space-time in the dimensional regularization. | ||
| - | |||
| - | For details see [[documentation:guide:calculating_one-loop_counterterms]] and the following tutorials: | ||
| - | * [[documentation:tutorials:vector_field]] | ||
| - | * [[documentation:tutorials:minimal_second_order_operator]] | ||
| - | * [[documentation:tutorials:minimal_fourth_order_operator]] | ||
| - | * [[documentation:tutorials:squared_vector_field]] | ||
| - | * [[documentation:tutorials:Gravity]] | ||
| - | ====Solving equations==== | ||
| - | Tensorial equations are often occur for example when one need to calculate propagator or find a projector operator etc. Redberry provides a function [[documentation:ref:Reduce]] which reduces a system of tensorial equations to a system of symbolic equations and allows to solve the last one with external "scalar" CAS. | ||
| - | |||
| - | For examples, see tutorials: | ||
| - | * [[documentation:tutorials:spin-3_propagator]] | ||
| - | * [[documentation:tutorials:Projectors for tensor particle]] | ||
| - | ====Dirac & SU(N) algebra==== | ||
| - | Redberry provides a set of common transformations needed for simplification expressions with Dirac and SU(N) matrices. | ||
| - | |||
| - | ===DiracTrace=== | ||
| - | evaluates trace of gamma matrices: | ||
| - | <sxh groovy; gutter: false> | ||
| - | defineMatrices 'G_m', 'G5', Matrix1.matrix | ||
| - | println DiracTrace[[Gamma: 'G_m']] >> 'Tr[G_m*G_n]'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > 4*g_{mn} | ||
| - | </sxh> | ||
| - | See [[documentation:ref:DiracTrace]]. | ||
| - | |||
| - | ---- | ||
| - | ====SpinorsSimplify==== | ||
| - | simplifies Dirac spinors: | ||
| - | <sxh groovy; gutter: false> | ||
| - | defineMatrices 'G_a', 'G5', Matrix1.matrix, 'cu', Matrix1.covector | ||
| - | def sSimplify = SpinorsSimplify[[uBar: 'cu', Momentum: 'p_a', Mass: 'm']] | ||
| - | println sSimplify >> 'cu*G^a*p_a'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > -m*cu*G_{b}+2*cu*p_{b} | ||
| - | </sxh> | ||
| - | See [[documentation:ref:SpinorsSimplify]]. | ||
| - | |||
| - | ---- | ||
| - | ===DiracSimplify=== | ||
| - | simplifies products of gamma matrices: | ||
| - | <sxh groovy; gutter: false> | ||
| - | defineMatrices 'G_a', 'G5', Matrix1.matrix | ||
| - | println DiracSimplify >> 'G5*G_a*G5*G_b*G^a*G^b'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > -8 | ||
| - | </sxh> | ||
| - | See [[documentation:ref:DiracSimpllify]]. | ||
| - | |||
| - | ---- | ||
| - | ===DiracOrder=== | ||
| - | order products of gamma matrices: | ||
| - | <sxh groovy; gutter: false> | ||
| - | defineMatrices 'G_a', 'G5', Matrix1.matrix | ||
| - | println DiracOrder >> 'G5*G_c*G_b*G_a'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > G_{a}*G_{b}*G_{c}*G5+2*G_{b}*G5*g_{ca}-2*G_{c}*G5*g_{ba}-2*G_{a}*G5*g_{cb} | ||
| - | </sxh> | ||
| - | See [[documentation:ref:DiracOrder]]. | ||
| - | |||
| - | ---- | ||
| - | ===LeviCivitaSimplify=== | ||
| - | simplifies combinations with Levi-Civita tensors: | ||
| - | <sxh groovy; gutter: false> | ||
| - | println LeviCivitaSimplify.minkowski['e_abcd'.t] >> 'e_abcm*e^abcn'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > -6*d_{m}^{n} | ||
| - | </sxh> | ||
| - | See [[documentation:ref: LeviCivitaSimplify]]. | ||
| - | |||
| - | ---- | ||
| - | ===setMandelstam=== | ||
| - | generates a list of mass shell and Mandelstam substitutions: | ||
| - | <sxh groovy; gutter: false> | ||
| - | def mandelstam = | ||
| - | setMandelstam([k1_a: 'm1', k2_a: 'm2', k3_a: 'm3', k4_a: 'm4']) | ||
| - | println mandelstam >> 'k1_a*k2^a + k3_b*k1^b'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > (1/2)*(-m2**2-m1**2+s)-(1/2)*(t-m3**2-m1**2) | ||
| - | </sxh> | ||
| - | See [[documentation:ref:setMandelstam]]. | ||
| - | |||
| - | ---- | ||
| - | ===UnitarySimplify=== | ||
| - | simplifies combinations of unitary matrices and SU(N) structural and $d$-constants | ||
| - | <sxh groovy; gutter: false> | ||
| - | defineMatrices 'T_A', Matrix2.matrix | ||
| - | println UnitarySimplify[[Matrix: 'T_A']] >> 'T_A*T^A'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > (1/2)*N**(-1)*(N**2-1) | ||
| - | </sxh> | ||
| - | See [[documentation:ref:UnitarySimplify]]. | ||
| - | |||
| - | ---- | ||
| - | ===UnitaryTrace=== | ||
| - | evaluates trace of unitary matrices: | ||
| - | <sxh groovy; gutter: false> | ||
| - | defineMatrices 'T_A', Matrix2.matrix | ||
| - | println UnitaryTrace[[Matrix: 'T_A']] >> 'Tr[T_A*T_B]'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > (1/2)*g_{BA} | ||
| - | </sxh> | ||
| - | See [[documentation:ref: UnitaryTrace]]. | ||
| - | |||
| - | For examples, see tutorials: | ||
| - | * [[documentation:tutorials:compton_scattering_in_qed]] | ||
| - | * [[documentation:tutorials:compton_scattering_in_qcd]] | ||
| - | * [[documentation:tutorials:b_c_to_u_bar_d_gamma|$B_c \to u \bar d \gamma$]] | ||
| - | ====See also==== | ||
| - | * Related guides: [[documentation:guide:list_of_transformations]], [[documentation:guide:calculating_one-loop_counterterms]], [[documentation:guide:programming_with_redberry]] | ||