Quantum mechanical path integrals in the first quantised approach to quantum field theory

Abstract

Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation theory. Here we review the history, main features and present applications of the formalism. Our emphasis is on recent developments such as the path integral representation of open fermion lines, the description of colour using auxiliary worldline fields, incorporation of higher spin, and extension of the formalism to non-commutative space.

13 Pages, 3 figures. Technical Report to be published in the proceedings of the workshop "Path Integration in Complex Dynamical Systems," Leiden, 6 Feb - 10 Feb 2017

References in corpus (89)

• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Massless Higher Spins and Holography
• Gauge Theory on Noncommutative Spaces
• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Field Theory Without Feynman Diagrams: One-Loop Effective Actions
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• One-Loop Corrections to Five-Gluon Amplitudes
• An Introduction to Noncommutative Spaces and their Geometry
• Worldline Instantons and Pair Production in Inhomogeneous Fields
• Deforming Einstein's Gravity
• Casimir Effect on the Worldline
• The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
• Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals
• Casimir effect for curved geometries: PFA validity limits
• Renormalisation of ϕ^4-theory on noncommutative R^2 in the matrix base
• String-Based Methods in Perturbative Gravity
• Pair production in inhomogeneous fields
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• Photon Splitting in a Strong Magnetic Field: Recalculation and Comparison With Previous Calculations
• Nonperturbative study of generalized ladder graphs in a ϕ^2χtheory
• Worldline formalism in a gravitational background
• Trace Anomalies from Quantum Mechanics
• The Refractive Index of Curved Spacetime: the Fate of Causality in QED
• Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production
• Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part I
• The Higher Derivative Expansion of the Effective Action by the String Inspired Method. Part II
• The Path Integral for a Particle in Curved Spaces and Weyl Anomalies
• Multidimensional Worldline Instantons
• Multiloop Calculations in the String-Inspired Formalism: The Single Spinor-Loop in QED
• Hyper-Kahler Calabi Metrics, L^2 Harmonic Forms, Resolved M2-branes, and AdS_4/CFT_3 Correspondence
• Quantum diffusion of magnetic fields in a numerical worldline approach
• Worldline Path Integrals for Fermions with Scalar, Pseudoscalar and Vector Couplings
• Spinning particles and higher spin fields on (A)dS backgrounds
• Dimensional regularization for N=1 susy sigma models and the worldline formalism
• Loop calculations in quantum-mechanical non-linear sigma models sigma models with fermions and applications to anomalies
• Second Order Fermions in Gauge Theories
• One loop photon-graviton mixing in an electromagnetic field: Part 1
• Two-loop self-dual Euler-Heisenberg Lagrangians (I): Real part and helicity amplitudes
• Loop calculations in quantum-mechanical non-linear sigma models
• Dynamically assisted Sauter-Schwinger effect - non-perturbative versus perturbative aspects
• Propagators and Path Integrals
• Gravitational corrections to the Euler-Heisenberg Lagrangian
• Particles with non abelian charges
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• Fermion-induced quantum action of vortex systems
• Spin Factor in Path Integral Representation for Dirac Propagator in External Fields
• Multiloop World-Line Green Functions from String Theory
• Worldline Green Functions for Arbitrary Feynman Diagrams
• Axial Couplings on the World-Line
• One-particle reducible contribution to the one-loop spinor propagator in a constant field
• Worldline path integral for the massive Dirac propagator : A four-dimensional approach
• Detours and Paths: BRST Complexes and Worldline Formalism
• Effective action for higher spin fields on (A)dS backgrounds
• On the trace anomaly of a Weyl fermion
• Multiphoton amplitudes and generalized LKF transformation in Scalar QED
• Bern-Kosower Rule for Scalar QED
• Scalar heat kernel with boundary in the worldline formalism
• Dressed scalar propagator in a non-abelian background from the worldline formalism
• Quantum effective actions from nonperturbative worldline dynamics
• Mode regularization, time slicing, Weyl ordering and phase space path integrals for quantum mechanical nonlinear sigma models
• Vacuum polarization tensor in inhomogeneous magnetic fields
• Dimensional regularization of nonlinear sigma models on a finite time interval
• U(N) spinning particles and higher spin equations on complex manifolds
• Master formulas for the dressed scalar propagator in a constant field
• On Mode Regularization of the Configuration Space Path Integral in Curved Space
• Vacuum Polarization in QED with World-Line Methods
• Extended SUSY quantum mechanics: transition amplitudes and path integrals
• String-inspired representations of photon/gluon amplitudes
• Quantum theories of (p,q)-forms
• A New Approach to Axial Vector Model Calculations II
• Quantum theory of massless (p,0)-forms
• Mixed symmetry Wilson-loop interactions in the worldline formalism
• Thermal Green's Functions from Quantum Mechanical Path Integrals II: Inclusion of Fermions
• Noncommutative U(1) gauge theory from a worldline perspective
• Non-Perturbative Mass Renormalization in Quenched QED from the Worldline Variational Approach
• Heat Trace Asymptotics on Noncommutative Spaces
• World-line techniques for resumming gluon radiative corrections at the cross-section level
• Unified theory in the worldline approach
• Trace anomalies and the string-inspired definition of quantum-mechanical path integrals in curved space
• Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part III
• The Fermion Content of the Standard Model
• U(N|M) quantum mechanics on Kaehler manifolds
• Worldline colour fields and non-Abelian quantum field theory
• Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies
• Asymptotic behavior of the QED perturbation series
• Hawking Radiation via Complex Geodesics
• On a New Method for Computing Trace Anomalies

Cited by in corpus (18)

• Advances in QED with intense background fields
• SUSY in the Sky with Gravitons
• Asymptotic dynamics on the worldline for spinning particles
• Lorentzian worldline path integral approach to Schwinger effect
• Color-kinematics duality from the Bern-Kosower formalism
• Effective action for delta potentials: spacetime-dependent inhomogeneities and Casimir self-energy
• QED as a many-body theory of worldlines: I. General formalism and infrared structure
• New Techniques for Worldline Integration
• Dressed Dirac Propagator from a Locally Supersymmetric $\mathcal{N}=1$ Spinning Particle
• Non-perturbative Quantum Propagators in Bounded Spaces
• Field redefinition invariant Lagrange multiplier formalism
• One-loop Amplitudes in the Worldline Formalism
• Worldline Modeling of Ultra-Intense Lasers for N-photon Scattering Processes
• Generalized LKF transformations for $N$-point fermion correlators in QED
• Superspace worldline formalism approach to Quantum Gravity: dimensional reduction and Holography
• Dimensional Regularization for the Particle Transition Amplitude in Curved Space
• Worldline Path Integrals for Gauge Fields and Quantum Computing
• What should be the ontology for the Standard Model?