Detours and Paths: BRST Complexes and Worldline Formalism

Abstract

We construct detour complexes from the BRST quantization of worldline diffeomorphism invariant systems. This yields a method to efficiently extract physical quantum field theories from particle models with first class constraint algebras. As an example, we show how to obtain the Maxwell detour complex by gauging N=2 supersymmetric quantum mechanics in curved space. Then we concentrate on first class algebras belonging to a class of recently introduced orthosymplectic quantum mechanical models and give generating functions for detour complexes describing higher spins of arbitrary symmetry types. The first quantized approach facilitates quantum calculations and we employ it to compute the number of physical degrees of freedom associated to the second quantized, field theoretical actions.

1+35 pages, 1 figure; typos corrected and references added, published version

References in corpus (38)

• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Nonlinear higher spin theories in various dimensions
• Gauge Invariances and Phases of Massive Higher Spins in (A)dS
• On higher spins and the tensionless limit of String Theory
• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Introduction to the Classical Theory of Higher Spins
• Higher Spin Gauge Theories in Various Dimensions
• Tensor gauge fields in arbitrary representations of GL(D,R) : duality & Poincare lemma
• Exotic tensor gauge theory and duality
• An Introduction to Free Higher-Spin Fields
• Worldline formalism in a gravitational background
• Tensor gauge fields in arbitrary representations of GL(D,R): II. Quadratic actions
• Parent field theory and unfolding in BRST first-quantized terms
• Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields
• Inconsistencies of Massive Charged Gravitating Higher Spins
• Worldline approach to vector and antisymmetric tensor fields
• Constant Curvature Algebras and Higher Spin Action Generating Functions
• Massless Poincare modules and gauge invariant equations
• Spinning particles and higher spin fields on (A)dS backgrounds
• Geometric Second Order Field Equations for General Tensor Gauge Fields
• The lagrangian description of representations of the Poincare group
• Dimensional regularization for N=1 susy sigma models and the worldline formalism
• On Massive Mixed Symmetry Tensor Fields in Minkowski Space and (A)dS
• Worldline approach to vector and antisymmetric tensor fields II
• Higher spin fields from a worldline perspective
• First Order Formalism for Mixed Symmetry Tensor Fields
• Mixed-symmetry massive fields in AdS(5)
• BRST treatment of zero modes for the worldline formalism in curved space
• U(N) spinning particles and higher spin equations on complex manifolds
• Yang-Mills detour complexes and conformal geometry
• Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras
• Kahler spinning particles
• The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra
• Higher Spin Gravitational Couplings and the Yang--Mills Detour Complex
• The B model as a twisted spinning particle
• (p,q)-form Kaehler Electromagnetism
• Conformal operators on forms and detour complexes on Einstein manifolds
• Conformally invariant operators, differential forms, cohomology and a generalisation of Q-curvature

Cited by in corpus (21)

• Unified BRST description of AdS gauge fields
• Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type
• FV-type action for AdS(5) mixed-symmetry fields
• General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic fields
• Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons
• Particles with non abelian charges
• General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. 2. Fermionic fields
• Effective action for higher spin fields on (A)dS backgrounds
• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Einstein gravity from the $\mathbb{N}=4$ spinning particle
• Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdS_d space
• Half-integer Higher Spin Fields in (A)dS from Spinning Particle Models
• Extended SUSY quantum mechanics: transition amplitudes and path integrals
• One-loop quantum gravity from the N=4 spinning particle
• Generalized Einstein Operator Generating Functions
• Quantum theories of (p,q)-forms
• BRST Detour Quantization
• Mixed symmetry Wilson-loop interactions in the worldline formalism
• U(N|M) quantum mechanics on Kaehler manifolds
• Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes
• Induced Action for Conformal Higher Spins from Worldline Path Integrals