Canonical path-integral quantization of yang-mills field theory with arbitrary external sources

Some modification of source terms is proposed for gauge field theories. In theSU(2) Yang-Mills theory with arbitrary external sources a canonical quantization procedure leads to a Lorentz-invariantS-matrix only when Fermi statistics is imposed on ghost fields. The usual source terms lead to a result that breaks Lorentz invariance and is singular when external chargesJskin0 vanish. The cases of the Abelian scalar electrodynamics and theSU(2) Yang-Mills field with external currents (Jskino=0,Jskini 0) are also discussed.     

Equivalence of stochastic quantization to field theories from supersymmetry

Using the Ward-Takahashi identities from the hidden supersymmetry in Langevin equation we present a very simple proof of the equivalence of stochastic quantization to field theories.     

Some stochastic aspects of quantization

From the advent of quantum mechanics, various types of stochastic-dynamical approach to quantum mechanics have been tried. We discuss how to utilize Nelson’s stochastic quantum mechanics to analyze the tunneling phenomena, how to derive relativistic field equations via the Poisson process and how to describe a quantum dynamics of open systems by the use of quantum state diffusion, or the stochastic Schrödinger equation.     

Chiral fermions in stochastic quantization

The simultaneous conservation of chiral and gauge currents in the framework of stochastic quantization is discussed. By means of the stochastic regularization procedure we explicitly compute the axial anomaly for fermions with mass m≠0 and the fictitious time t→∞. However, when m≡0, an ambiguity appears: it turns out that the two limits (m→0, t→∞) do not commute. In this case non-perturbative methods show that the difference between left-handed and right-handed zero modes cancels; therefore no anomaly is present and stochastic regularization is unable to describe chiral theories at finite fictitious time. It is in any case unclear how stochastic quantization can describe a massless fermion at finite t.     

Real-time gauge theory simulations from stochastic quantization with optimized updating

We investigate simulations for gauge theories on a Minkowskian space–time lattice. We employ stochastic quantization with optimized updating using stochastic reweighting or gauge fixing, respectively. These procedures do not affect the underlying theory but strongly improve the stability properties of the stochastic dynamics, such that simulations on larger real-time lattices can be performed.     

Real-time gauge theory simulations from stochastic quantization with optimized updating

Stochastic quantisation is applied to the problem of calculating real-time evolution on a Minkowskian space-time lattice. We employ optimized updatig using reweighting, or gauge fixing, respectively. These procedures do not affect the underlying theory, but strongly improve the stability properties of the stochastic dynamics.     

Relating field theories via stochastic quantization

This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the quantization method used to obtain the quantum crystal is a discrete analog of stochastic quantization. This model is of interest for string theory, since the (classical) melting crystal corner is related to the topological A-model. We outline several ideas for interpreting the quantum crystal on the string theory side of the correspondence, exploring interpretations in the Wheeler–De Witt framework and in terms of a non-Lorentz invariant limit of topological M-theory.     

Nonlocal stochastic quantization of scalar electrodynamics

Quantization of the electromagnetic interactions of scalar charged particles is considered within the stochastic Langevin and Schwinger-Dyson equations with nonlocal white noise. Fulfillment of the gauge-invariant condition in such a scheme is studied in detail. Matrix elements of the vacuum polarization and self-energy diagrams of the scalar electrodynamics are calculated explicitly, which reduce to usual nonlocal scalar electrodynamic results.     

Simplified large-N limit in stochastic quantization

In the large-N limit,O(N)-invariant models become exactly soluble due to factorization properties first emphasized by Migdal and Witten. It is shown that in this limit, the Langevin equation of stochastic quantization offers a direct and simple determination of the mass gap. The method is applied to different bosonic and fermionic models.     

Conserved Noether currents in stochastic quantization

A general procedure for constructing Noether conserved currents in the stochastic quantization scheme corresponding to symmetries of the equilibrium theory is proposed. Two different regularizations — the Breit-Gupta-Zaks stochastic time regularization and a new supersymmetric regularization — are employed, and the origin of chiral anomalies is exhibited in this framework.     

Oscillating gravity,non-singularity and mass quantization from Moffat stochastic gravity arguments

In Moffat stochastic gravity arguments, the spacetime geometry is assumed to be a fluctuating background and the gravitational constant is a control parameter due to the presence of a time-dependent Gaussian white noise $\xi (t).$ In such a surrounding, both the singularities of gravitational collapse and the Big Bang have a zero probability of occurring. In this communication, we generalize Moffat's arguments by adding a random temporal tiny variable for a smoothing purpose and creating a white Gaussian noise process with a short correlation time. The Universe accordingly is found to be non-singular and is dominated by an oscillating gravity. A connection with a quantum oscillator was established and analyzed. Surprisingly, the Hubble mass which emerges in extended supergravity may be quantized.     

Ward identities and chiral anomalies in stochastic quantization

We derive the Ward identities (WI) for vector and axial currents in stochastic quantization at any given fictitious time t. This is achieved through a functional integral representation of the fermionic Langevin equations. The currents for this effective field theory differ in general from the naive ones; if stochastic regularization is used they are both conserved. We establish the connection between those WI and the field theory ones. The physical source of chiral anomalies is identified: these result from the quantum fluctuations in the fictitious time evolution of the system. In this context, both a traditional regularization method (Pauli-Villars) and stochastic regularization are considered.