Searcharxiv⌕ Search

arXiv subjects

M. P. Fry

Publications and source records attributed to M. P. Fry.

17 recordsLinked to original sources
arXiv2020

Non-perturbative path integral quantization of the electroweak model: the Maxwell integration

The non-perturbative path integral quantization of the electroweak model is confronted with an apparent instability when integrating over the Maxwell potential $A_μ$ due to the fast growth of the box graphs $AAAA$ and $AAAZ$ for large amplitude variations of $A_μ$. $Z_μ$ is from the vector part of the weak neutral current. These graphs are unavoidable because they are conditionally convergent and have to be isolated in the model's exact Euclidean one-loop effective action arising from its fermion determinants. A previous QED calculation of the large amplitude variation of its fermion determinant for a class of random potentials showed that the $AAAA$ box graph cancels in this limit. Using this result it is shown that within the electroweak model large amplitude variations of $A_μ$ for fixed $Z_μ$ in a superposition of these fields cancel the $AAAA$ and $AAAZ$ graphs, thereby removing an apparent obstacle to the model's non-perturbative quantization. A negative paramagnetic term in the remainder opposes the effective action's growth for such variations. Its calculation requires knowledge of the degeneracy of the bound states of a charged fermion in the four-dimensional magnetic fields generated by the functional measure of $A_μ$.

hep-th↗
arXiv2019

Strong, Random field behavior of the Euclidean Dirac propagator

The one-loop effective action of quantum electrodynamics in four dimensions is shown to be controlled by the Euclidean Dirac propagator $G$ in a background potential. After separating the photon self-energy and photon-photon scattering graphs from the effective action the remainder is known to be the logarithm of an entire function of the electric charge of order 4 under mild regularity assumptions on the potential. This input together with QED's lack of an ultrastable vacuum constrain the strong field behavior of $G$. It is shown that $G$ vanishes in the strong field limit. The relevance of this result to the decoupling of QED from the remainder of the electroweak model for large amplitude variations of the Maxwell field is discussed.

hep-th↗
arXiv2015

Non-perturbative quantization of the electroweak model's electrodynamic sector

Consider the Euclidean functional integral representation of any physical process in the electroweak model. Integrating out the fermion degrees of freedom introduces twenty-four fermion determinants. These multiply the Gaussian functional measures of the Maxwell, $Z$, $W$ and Higgs fields to give an effective functional measure. Suppose the functional integral over the Maxwell field is attempted first. This paper is concerned with the large amplitude behavior of the Maxwell effective measure. It is assumed that the large amplitude variation of this measure is insensitive to the presence of the $Z$, $W$ and $H$ fields; they are assumed to be a subdominant perturbation of the large amplitude Maxwell sector. Accordingly, we need only examine the large amplitude variation of a single QED fermion determinant. To facilitate this the Schwinger proper time representation of this determinant is decomposed into a sum of three terms. The advantage of this is that the separate terms can be non-perturbatively estimated for a measurable class of large amplitude random fields in four dimensions. It is found that the QED fermion determinant grows faster than $\exp \left[ce^2\int\mathrm d^4x\, F_{μν}^2\right]$, $c>0$, in the absence of zero mode supporting random background potentials. This raises doubt on whether the QED fermion determinant is integrable with any Gaussian measure whose support does not include zero mode supporting potentials. Including zero mode supporting background potentials can result in a decaying exponential growth of the fermion determinant. This is \textit{prima facie} evidence that Maxwellian zero modes are necessary for the non-perturbative quantization of QED and, by implication, for the non-perturbative quantization of the electroweak model.

hep-th↗
arXiv2012

Stability of QED

It is shown for a class of random, time-independent, square-integrable, three-dimensional magnetic fields that the one-loop effective fermion action of four-dimensional QED increases faster than a quadratic in B in the strong coupling limit. The limit is universal. The result relies on the paramagnetism of charged spin - 1/2 fermions and the diamagnetism of charged scalar bosons.

hep-th↗
arXiv2010

Nonperturbative results for the mass dependence of the QED fermion determinant

The fermion determinant in four-dimensional quantum electrodynamics in the presence of O(2)XO(3) symmetric background gauge fields with a nonvanishing global chiral anomaly is considered. It is shown that the leading mass singularity of the determinant's nonperturbative part is fixed by the anomaly. It is also shown that for a large class of such fields there is at least one value of the fermion mass at which the determinant's nonperturbative part reduces to its noninteracting value.

hep-th↗
arXiv2010

Evidence for mass zeros of the fermionic determinant in four-dimensional quantum electrodynamics

The Euclidean fermionic determinant in four-dimensional quantum electrodynamics is considered as a function of the fermionic mass for a class of $O(2)\times O(3)$ symmetric background gauge fields. These fields result in a determinant free of all cutoffs. Consider the one-loop effective action, the logarithm of the determinant, and subtract off the renormalization dependent second-order term. Suppose the small-mass behavior of this remainder is fully determined by the chiral anomaly. Then either the remainder vanishes at least once as the fermionic mass is varied in the interval $0 < m < \infty$ or it reduces to its fourth-order value in which case the new remainder, obtained after subtracting the fourth-order term, vanishes at least once. Which possibility is chosen depends on the sign of simple integrals involving the field strength tensor and its dual.

hep-th↗
arXiv2005

Mass zeros in the one-loop effective actions of QED in 1+1 and 3+1 dimensions

It is known that the one-loop effective action of ${QED}_2$ is a quadratic in the field strength when the fermion mass is zero: all potential higher order contributions beyond second order vanish. For nonzero fermion mass it is shown that this behavior persists for a general class of fields for at least one value of the fermion mass when the external field's flux $Φ$ satisfies $0<|eΦ|<2π$. For ${QED}_4$ the mass-shell renormalized one-loop effective action vanishes for at least one value of the fermion mass for a class of smooth, square integrable background gauge fields provided a plausible zero-mass limit exists.

hep-th↗
arXiv2004

Fermion Determinants: Some Recent Analytic Results

The use of known analytic results for the continuum fermion determinants in QCD and QED as benchmarks for zero lattice spacing extrapolations of lattice fermion determinants is proposed. Specifically, they can be used as a check on the universality hypothesis relating the continuum limits of the na\"ıve, staggered and Wilson fermion determinants.

hep-lat↗
arXiv2003

Fermion Determinants 2003

It is recommended that lattice QCD representations of the fermion determinant, including the discretization of the Dirac operator, be checked in the continuum limit against known QED determinant results. Recent work on the massive QED fermion determinant in two dimensions is reviewed. A feasible approach to the four-dimensional QED determinant with O(2) x O(3) symmetric background fields is briefly discussed.

hep-th↗
arXiv2003

Fermion determinant for general background gauge fields

An exact representation of the Euclidean fermion determinant in two dimensions for centrally symmetric, finite-ranged Abelian background fields is derived. Input data are the wave function inside the field's range and the scattering phase shift with their momenta rotated to the positive imaginary axis and fixed at the fermion mass for each partial-wave. The determinant's asymptotic limit for strong coupling and small fermion mass for square-integrable, unidirecitonal magnetic fields is shown to depend only on the chiral anomaly. The concept of duality is extended from one to two-variable fields, thereby relating the two-dimensional Euclidean determinant for a class of background magnetic fields to the pair production probability in four dimensions for a related class of electric pulses. Additionally, the ``diamagnetic'' bound on the two-dimensional Euclidean determinant is related to the negative sign of dImS_eff/dm^2 in four dimensions in the strong coupling, small mass limit, where S_eff is the one-loop effective action.

hep-th↗
arXiv2001

Fermion Determinants

The current status of bounds on and limits of fermion determinants in two, three and four dimensions in QED and QCD is reviewed. A new lower bound on the two-dimensional QED determinant is derived. An outline of the demonstration of the continuity of this determinant at zero mass when the background magnetic field flux is zero is also given.

hep-th↗
arXiv2000

Chiral limit of the two-dimensional fermionic determinant in a general magnetic field

We consider the effective action for massive two-dimensional QED in flat Euclidean space-time in the background of a general square-integrable magnetic field with finite range. It is shown that its small mass limit is controlled by the chiral anomaly. New results for the low-energy scattering of electrons in 2+1 dimensions in static, inhomogenous magnetic fields are also presented.

hep-th↗
arXiv1996

QED in inhomogeneous magnetic fields

A lower bound is placed on the fermionic determinant of Euclidean quantum electrodynamics in three dimensions in the presence of a smooth, finite--flux, static, unidirectional magnetic field $\mathbf{B}(\mathbf{r})=(0,0,B(\mathbf{r}))$, where $B(\mathbf{r})\geq 0$ or $B(\mathbf{r})\leq 0$ and $\mathbf r$ is a point in the $xy\mbox{-plane}$. Bounds are also obtained for the induced spin for $2+1$ dimensional QED in the presence of $\mathbf{B}(\mathbf{r})$. An upper bound is placed on the fermionic determinant of Euclidean QED in four dimensions in the presence of a strong, static, directionally-varying, square-integrable magnetic field $\mathbf{B}(\mathbf{r})$ on $\R^3 $.

hep-th↗
arXiv1995

QED in strong, finite-flux magnetic fields

Lower bounds are placed on the fermionic determinants of Euclidean quantum electrodynamics in two and four dimensions in the presence of a smooth, finite-flux, static, unidirectional magnetic field $B(r) =(0,0,B(r))$, where $B(r) \geq 0$ or $B(r) \leq 0$, and $r$ is a point in the xy-plane.

hep-th↗
arXiv1994

Fermion Determinants in Static, Inhomogeneous Magnetic Fields

The renormalized fermionic determinant of QED in 3 + 1 dimensions, $\mbox{det}_{ren}$, in a static, unidirectional, inhomogeneous magnetic field with finite flux can be calculated from the massive Euclidean Schwinger model's determinant, $\mbox{det}_{Sch}$, in the same field by integrating $\mbox{det}_{Sch}$, over the fermion's mass. Since $\mbox{det}_{ren}$ for general fields is central to QED, it is desirable to have nonperturbative information on this determinant, even for the restricted magnetic fields considered here. To this end we continue our study of the physically relevant determinant $\mbox{det}_{Sch}$. It is shown that the contribution of the massless Schwinger model to $\mbox{det}_{Sch}$ is cancelled by a contribution from the massive sector of QED in 1 + 1 dimensions and that zero modes are suppressed in $\mbox{det}_{Sch}$. We then calculate $\mbox{det}_{Sch}$ analytically in the presence of a finite flux, cylindrical magnetic field. Its behaviour for large flux and small fermion mass suggests that the zero-energy bound states of the two-dimensional Pauli Hamiltonian are the controlling factor in the growth of $\ln \mbox{det}_{Sch}$. Evidence is presented that $\mbox{det}_{Sch}$ does not converge to the determinant of the massless Schwinger model in the small mass limit for finite, nonzero flux magnetic fields.

hep-th↗
arXiv1993

Fermionic Determinant of the Massive Schwinger Model

A representation for the fermionic determinant of the massive Schwinger model, or $QED_2$, is obtained that makes a clean separation between the Schwinger model and its massive counterpart. From this it is shown that the index theorem for $QED_2$ follows from gauge invariance, that the Schwinger model's contribution to the determinant is canceled in the weak field limit, and that the determinant vanishes when the field strength is sufficiently strong to form a zero-energy bound state.

hep-th↗