Worldline Path Integrals for Fermions with Scalar, Pseudoscalar and Vector Couplings

Abstract

A systematic derivation is given of the worldline path integrals for the effective action of a multiplet of Dirac fermions interacting with general matrix-valued classical background scalar, pseudoscalar, and vector gauge fields. The first path integral involves worldline fermions with antiperiodic boundary conditions on the worldline loop and generates the real part of the one loop (Euclidean) effective action. The second path integral involves worldline fermions with periodic boundary conditions and generates the imaginary part of the (Euclidean) effective action, i.e. the phase of the fermion functional determinant. Here we also introduce a new regularization for the phase of functional determinants resembling a heat-kernel regularization. Compared to the known special cases, our worldline Lagrangians have a number of new interaction terms; the validity of some of these terms is checked in perturbation theory. In particular, we obtain the leading order contribution (in the heavy mass expansion) to the Wess-Zumino-Witten term, which generates the chiral anomaly.

23 pages, Plain Tex, no macros needed, some minor changes and some references added

References in corpus (3)

• Worldline Green Functions for Multiloop Diagrams
• Second Order Fermions in Gauge Theories
• Yukawa Couplings for the Spinning Particle and the World Line Formalism

Cited by in corpus (59)

• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals
• Semi-classical transport theory for non-Abelian plasmas
• Worldline formalism in a gravitational background
• The chiral anomaly, Berry's phase and chiral kinetic theory, from world-lines in quantum field theory
• Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part I
• Deeply inelastic scattering structure functions on a hybrid quantum computer
• World-line construction of a covariant chiral kinetic theory
• Refining the Proof of Planar Equivalence
• Quantum diffusion of magnetic fields in a numerical worldline approach
• Dimensional regularization for N=1 susy sigma models and the worldline formalism
• Worldline Path Integrals for Fermions with General Couplings
• Loop calculations in quantum-mechanical non-linear sigma models sigma models with fermions and applications to anomalies
• Covariant technique of derivative expansion of one-loop effective action
• Constructing phase space distributions with internal symmetries
• Wong's equations and the small x effective action in QCD
• The role of the chiral anomaly in polarized deeply inelastic scattering I: Finding the triangle graph inside the box diagram in Bjorken and Regge asymptotics
• Axial Couplings on the World-Line
• Worldline path integral for the massive Dirac propagator : A four-dimensional approach
• Sizable CP Violation in the Bosonized Standard Model
• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Discrete worldline instantons
• The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics
• World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory
• Minding one's P's and Q's : from the one loop effective action in quantum field theory to classical transport theory
• Path Integrals and Pseudoclassical Description for Spinning Particles in Arbitrary Dimensions
• Magnetic Interactions of D-branes and Wess-Zumino Terms in Super Yang-Mills Effective Actions
• Calculation of 1-loop Hexagon Amplitudes in the Yukawa Model
• Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes
• String-inspired representations of photon/gluon amplitudes
• Lattice Study of Planar Equivalence: The Quark Condensate
• On phase transitions in two-dimensional disordered systems
• Finite temperature Schwinger pair production in coexistent electric and magnetic fields
• Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part II
• Pure bosonic worldline path integral representation for fermionic determinants, non-Abelian Stokes theorem, and quasiclassical approximation in QCD
• Structure functions at small x from world-lines. I: Unpolarized distributions
• Nonlinear dynamics of soft fermion excitations in hot QCD plasma III: Soft-quark bremsstrahlung and energy losses
• QED as a many-body theory of worldlines: I. General formalism and infrared structure
• Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part III
• Hard Thermal Loops and Beyond in the Finite Temperature World-Line Formulation of QED
• Effective Action in a General Chiral Model: Next to Leading Order Derivative Expansion in the Worldline Method
• New Techniques for Worldline Integration
• Pinched Gluon Vertex Operator in Super-Worldline Formalism
• Integral representations of thermodynamic 1PI Green functions in the world-line formalism
• Geometry of spin-field coupling on the worldline
• Worldline approach for spinor fields in manifolds with boundaries
• Boundary $\sigma$-model and corrections to D-brane actions
• Siegel superparticle, higher order fermionic constraints, and path integrals
• The equations of motion for a classical color particle in background non-Abelian bosonic and fermionic fields
• Non-Perturbative One-Loop Effective Action for QED with Yukawa Couplings
• Renormalization of Boundary Fermions and World-Volume Potentials on D-branes
• Mapping between the classical and pseudoclassical models of a relativistic spinning particle in external bosonic and fermionic fields. I
• Unitary quantization and para-Fermi statistics of order two
• Electric Field Decay Without Pair Production: Lattice, Bosonization and Novel Worldline Instantons
• Euler-Heisenberg Lagrangian under an axial gauge field
• New tests and applications of the worldline path integral in the first order formalism
• Worldlines on Orbifolds and the Fayet-Iliopoulos Term
• Mapping between the classical and pseudoclassical models of a relativistic spinning particle in external bosonic and fermionic fields. II
• Fermions in worldline holography