Searcharxiv⌕ Search

arXiv subjects

Gary McCartor

Publications and source records attributed to Gary McCartor.

16 recordsLinked to original sources
arXiv2005

Perturbative Formulation of Pure Space-Like Axial Gauge QED with Infrared Divergences Regularized by Residual Gauge Fields

We construct a new perturbative formulation of pure space-like axial gauge QED in which the inherent infrared divergences are regularized by residual gauge fields. For that purpose we perform our calculations in coordinates $x^μ=(x^+,x^-,x^1,x^2)$, where $x^+=x^0\sinθ+x^3\cos θ$ and $x^-=x^0\cosθ-x^3\sinθ$. $A_-=A^0\cosθ+A^3 \sinθ=n{\cdot}A=0$ is taken as the gauge fixing condition. We show in detail that, in perturbation theory, infrared divergences resulting from the residual gauge fields cancel infrared divergences resulting from the physical parts of the gauge field. As a result we obtain the gauge field propagator prescribed by Mandelstam and Leibbrandt. By taking the limit $θ{\to} \fracπ{4}$ we can construct the light-cone formulation which is free from infrared difficulty. With that analysis complete, we perform a successful calculation of the one loop electron self energy, something not previously done in light-cone quantization and light-cone gauge.

hep-th↗
arXiv2004

Extended Hamiltonian Formalism of the Pure Space-Like Axial Gauge Schwinger Model II

Canonical methods are not sufficient to properly quantize space-like axial gauges. In this paper, we obtain guiding principles which allow the construction of an extended Hamiltonian formalism for pure space-like axial gauge fields. To do so, we clarify the general role residual gauge fields play in the space-like axial gauge Schwinger model. In all the calculations we fix the gauge using a rule, $n{\cdot}A=0$, where $n$ is a space-like constant vector and we refer to its direction as $x_-$. Then, to begin with, we construct a formulation in which the quantization surface is space-like but not parallel to the direction of $n$. The quantization surface has a parameter which allows us to rotate it, but when we do so we keep the direction of the gauge field fixed. In that formulation we can use canonical methods. We bosonize the model to simplify the investigation. We find that the antiderivative, $({\partial}_-)^{-1}$, is ill-defined whatever quantization coordinates we use as long as the direction of $n$ is space-like. We find that the physical part of the dipole ghost field includes infrared divergences. However, we also find that if we introduce residual gauge fields in such a way that the dipole ghost field satisfies the canonical commutation relations, then the residual gauge fields are determined so as to regularize the infrared divergences contained in the physical part. The propagators then take the form prescribed by Mandelstam and Leibbrandt. We make use of these properties to develop guiding principles which allow us to construct consistent operator solutions in the pure space-like case where the quantization surface is parallel to the direction of $n$ and canonical methods do not suffice.

hep-th↗
arXiv2003

Calculations in the Light-Cone Representation

For the problem of calculating bound states in quantum field theory, the light-cone representation offers advantages over the more common equal-time representation. It also has subtleties and disadvantages compared to the equal-time representation. If current efforts to use the light-cone representation to solve for the properties of hadrons in QCD are to succeed, at least two problems have to be solved: we must find the induced operators; we must develop an effective procedure of regularization and renormalization. In this paper I will try to explain what an induced operator is and say what we know about them and will report on recent attempts to develop an effective procedure of regularization and renormalization.

hep-th↗
arXiv2000

Chiral Symmetry {\it Breaking} in the Light-Cone Representation ($M_π^2 \sim μ_q <Ω|\barψψ|Ω> +...$)

In this paper I shall discuss the way in which vacuum structure and condensates occur in the light-cone representation. I shall particularly emphasize the mechanism by which the mass squared of a composite such as the pion comes to depend linearly on the bare mass of its Fermion constituents. I shall give details in two dimensions then discuss the case of four dimensions more speculatively.

hep-th↗
arXiv2000

Regulating the $P^+ = 0$ Singularity

I shall discuss the regulation of the $P^+ = 0$ singularity and give some examples. Regulating the singularity induces new operators into the theory. This process seems rather different for the case of ultraviolet singularities than for the case of infrared singularities.

hep-th↗
arXiv1999

1+1 Gauge Theories in the Light-Cone Representation

We present a representation independent solution to the continuum Schwinger model in light-cone ($A^+ = 0$) gauge. We then discuss the problem of finding that solution using various quantization schemes. In particular we shall consider equal-time quantization and quantization on either characteristic surface, $x^+ = 0$ or $x^- = 0$.

hep-th↗
arXiv1999

Application of Pauli-Villars Regularization and Discretized Light-Cone Quantization to a (3+1)-Dimensional Model

We apply Pauli-Villars regularization and discrete light-cone quantization to the nonperturbative solution of a (3+1)-dimensional model field theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of the complex symmetric Lanczos algorithm. This permits the calculation of each Fock-sector wave function, and from these we obtain values for various quantities, such as average multiplicities and average momenta of constituents, structure functions, and a form factor slope.

hep-ph↗
arXiv1999

The Indispensability of Ghost Fields in the Light-Cone Gauge Quantization of Gauge Fields

We continue McCartor and Robertson's recent demonstration of the indispensability of ghost fields in the light-cone gauge quantization of gauge fields. It is shown that the ghost fields are indispensable in deriving well-defined antiderivatives and in regularizing the most singular component of gauge field propagator. To this end it is sufficient to confine ourselves to noninteracting abelian fields. Furthermore to circumvent dealing with constrained systems, we construct the temporal gauge canonical formulation of the free electromagnetic field in auxiliary coordinates $x^μ=(x^-,x^+,x^1,x^2)$ where $x^-=x^0 cosθ-x^3 sinθ, x^+=x^0 sinθ+x^3 cosθ$ and $x^-$ plays the role of time. In so doing we can quantize the fields canonically without any constraints, unambiguously introduce "static ghost fields" as residual gauge degrees of freedom and construct the light-cone gauge solution in the light-cone representation by simply taking the light-cone limit ($θ\to π/4$). As a by product we find that, with a suitable choice of vacuum the Mandelstam-Leibbrandt form of the propagator can be derived in the $θ=0$ case (the temporal gauge formulation in the equal-time representation).

hep-th↗
arXiv1999

Light-Cone Quantization of the Schwinger Model

We consider constructing a canonical quantum theory of the light-cone gauge ($A_-$=0) Schwinger model in the light-cone representation. Quantization conditions are obtained by requiring that translational generators $P_+$ and $P_-$ give rise to Heisenberg equations which, in a physical subspace, are consistant with the field equations. A consistent operator solution with residual gauge degrees of freedom is obtained by solving initial value problems on the light-cones. The construction allows a parton picture although we have a physical vacuum with nontrivial degeneracies in the theory.

hep-th↗
arXiv1998

The Mass Operator in the Light-Cone Representation

I argue that for the case of fermions with nonzero bare mass there is a term in the matter density operator in the light-cone representation which has been omitted from previous calculations. The new term provides agreement with previous results in the equal-time representation for mass perturbation theory in the massive Schwinger model. For the DLCQ case the physics of the new term can be represented by an effective operator which acts in the DLCQ subspace, but the form of the term might be hard to guess and I do not know how to determine its coefficient from symmetry considerations.

hep-th↗
arXiv1997

Subtleties in the Light-Cone Representation

To produce an isomorphism between the light-cone and equal-time representations some additional formalism beyond that originally proposed for the light-cone representation may sometimes be required. The additional formalism usually involves zero modes and is most likely to affect delicate, high energy aspects of the solution such as condensates. In this talk I will review some of the information which has been obtained in the past few years on these issues with particular emphasis on the Schwinger model as an example.

hep-th↗
arXiv1996

Some Lessons from the Schwinger Model

I shall recall a number of solutions to the Schwinger model in different gauges, having different boundary conditions and using different quantization surfaces. I shall discuss various properties of these solutions emphasizing the degrees of freedom necessary to represent the solution, the way the operator products are defined and the effects these features have on the chiral condensate.

hep-th↗
arXiv1995

The Mandelstam-Leibbrandt Prescription in Light-Cone Quantized Gauge Theories

Quantization of gauge theories on characteristic surfaces and in the light-cone gauge is discussed. Implementation of the Mandelstam-Leibbrandt prescription for the spurious singularity is shown to require two distinct null planes, with independent degrees of freedom initialized on each. The relation of this theory to the usual light-cone formulation of gauge field theory, using a single null plane, is described. A connection is established between this formalism and a recently given operator solution to the Schwinger model in the light-cone gauge.

hep-th↗
arXiv1994

Schwinger Model in the Light-Cone Representation

I present a solution to the Schwinger model in the light-cone representation which corrects an error in a previous work. I emphasize the details of the mechanism by which the physical vacuum is different than the perturbative vacuum. I suggest that the method of analyzing vacuum structure presented here may be of use in more complicated theories such as QCD.

hep-th↗
arXiv1993

Light-Cone Quantization of Gauge Fields

Light-cone quantization of gauge field theory is considered. With a careful treatment of the relevant degrees of freedom and where they must be initialized, the results obtained in equal-time quantization are recovered, in particular the Mandelstam-Leibbrandt form of the gauge field propagator. Some aspects of the ``discretized'' light-cone quantization of gauge fields are discussed.

hep-th↗