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Fred Cooper

Publications and source records attributed to Fred Cooper.

At least 73 records · Page 4Linked to original sources
arXiv2009

Shift Theorem Involving the Exponential of a Sum of Non-Commuting Operators in Path Integrals

We consider expressions of the form of an exponential of the sum of two non-commuting operators of a single variable inside a path integration. We show that it is possible to shift one of the non-commuting operators from the exponential to other functions which are pre-factors and post-factors when the domain of integration of the argument of that function is from -\infty to +\infty. This shift theorem is useful to perform certain integrals and path integrals involving the exponential of sum of two non-commuting operators.

hep-th↗
arXiv2009

Backreaction and Particle Production in (3+1)-dimensional QED

We study the fermion pair production from a strong electric field in boost-invariant coordinates in (3+1) dimensions and exploit the cylindrical symmetry of the problem. This problem has been used previously as a toy model for populating the central-rapidity region of a heavy-ion collision (when we can replace the electric by a chromoelectric field). We derive and solve the renormalized equations for the dynamics of the mean electric field and current of the produced particles, when the field is taken to be a function only of the fluid proper time $τ= \sqrt{t^2-z^2}$. We determine the proper-time evolution of the comoving energy density and pressure of the ensuing plasma and the time evolution of suitable interpolating number operators. We find that unlike in (1+1) dimensions, the energy density closely follows the longitudinal pressure. The transverse momentum distribution of fermion pairs at large momentum is quite different and larger than that expected from the constant field result.

hep-ph↗
arXiv2009

On the forward cone quantization of the Dirac field in "longitudinal boost-invariant" coordinates with cylindrical symmetry

We obtain a complete set of free-field solutions of the Dirac equation in a (longitudinal) boost-invariant geometry with azimuthal symmetry and use these solutions to perform the canonical quantization of a free Dirac field of mass $M$. This coordinate system which uses the 1+1 dimensional fluid rapidity $η= 1/2 \ln [(t-z)/(t+z)]$ and the fluid proper time $τ= (t^2-z^2)^{1/2}$ is relevant for understanding particle production of quarks and antiquarks following an ultrarelativistic collision of heavy ions, as it incorporates the (approximate) longitudinal "boost invariance" of the distribution of outgoing particles. We compare two approaches to solving the Dirac equation in curvilinear coordinates, one directly using Vierbeins, and one using a "diagonal" Vierbein representation.

hep-ph↗
arXiv2009

Top Quark Production from Black Holes at the CERN LHC

LHC is expected to be a top quark factory. If the fundamental Planck scale is near a TeV, then we also expect the top quarks to be produced from black holes via Hawking radiation. In this paper we calculate the cross sections for top quark production from black holes at the LHC and compare it with the direct top quark cross section via parton fusion processes at next-to-next-to-leading order (NNLO). We find that the top quark production from black holes can be larger or smaller than the pQCD predictions at NNLO depending upon the Planck mass and black hole mass. Hence the observation of very high rates for massive particle production (top quarks, higgs or supersymmetry) at the LHC may be an useful signature for black hole production.

hep-ph↗
arXiv2008

Casimir dependence of transverse distribution of pairs produced from a strong constant chromo-electric background field

The transverse distribution of gluon and quark-antiquark pairs produced from a strong constant chromo-electric field depends on two gauge invariant quantities, $C_1=E^aE^a$ and $C_2=[d_{abc}E^aE^bE^c]^2$, as shown earlier in [G.C. Nayak and P. van Nieuwenhuizen, Phys. Rev. D 71, 125001 (2005)] for gluons and in [G.C. Nayak, Phys. Rev. D 72, 125010 (2005)] for quarks. Here, we discuss the explicit dependence of the distribution on the second Casimir invariant, C_2, and show the dependence is at most a 15% effect.

hep-ph↗
arXiv2008

Fermion pair production in QED and the backreaction problem in (1+1)-dimensional boost-invariant coordinates revisited

We study two different initial conditions for fermions for the problem of pair production of fermions coupled to a classical electromagnetic field with backreaction in \oneplusone boost-invariant coordinates. Both of these conditions are consistent with fermions initially in a vacuum state. We present results for the proper time evolution of the electric field $E$, the current, the matter energy density, and the pressure as a function of the proper time for these two cases. We also determine the interpolating number density as a function of the proper time. We find that when we use a "first order adiabatic" vacuum initial condition or a "free field" initial condition for the fermion field, we obtain essentially similar behavior for physically measurable quantities. The second method is computationally simpler, it is twice as fast and involves half the storage required by the first method.

hep-ph↗
arXiv2008

Compactons in PT-symmetric generalized Korteweg-de Vries Equations

In an earlier paper Cooper, Shepard, and Sodano introduced a generalized KdV equation that can exhibit the kinds of compacton solitary waves that were first seen in equations studied by Rosenau and Hyman. This paper considers the PT-symmetric extensions of the equations examined by Cooper, Shepard, and Sodano. From the scaling properties of the PT-symmetric equations a general theorem relating the energy, momentum, and velocity of any solitary-wave solution of the generalized KdV equation is derived, and it is shown that the velocity of the solitons is determined by their amplitude, width, and momentum.

math-ph↗
arXiv2006

Schwinger Mechanism for Fermion Pair Production in the Presence of Arbitrary Time Dependent Background Electric Field

We study the Schwinger mechanism for the pair production of fermions in the presence of an arbitrary time-dependent background electric field E(t) by directly evaluating the path integral. We obtain an exact non-perturbative result for the probability of fermion-antifermion pair production per unit time per unit volume per unit transverse momentum (of the fermion or antifermion) from the arbitrary time dependent electric field E(t) via Schwinger mechanism. We find that the exact non-perturbative result is independent of all the time derivatives d^nE(t)/dt^n, where n=1,2,....\infty. This result has the same functional dependence on E as the Schwinger's constant electric field E result with the replacement: E -> E(t).

hep-th↗
arXiv2006

Schwinger Mechanism in the Presence of Arbitrary Time Dependent Background Electric Field

We study, for the first time, the Schwinger mechanism for the pair production of charged scalars in the presence of an arbitrary time-dependent background electric field E(t) by by directly evaluating the path integral. We obtain an exact non-perturbative result for the probability of charged scalar particle-antiparticle pair production per unit time per unit volume per unit transverse momentum (of the particle or antiparticle) from the arbitrary time dependent electric field E(t). We find that the exact non-perturbative result is independent of all the time derivatives d^nE(t)/dt^n, where n=1,2,....\infty. This result has the same functional dependence on E as the constant electric field E result with the replacement: E -> E(t).

hep-th↗
arXiv2006

Non-Perturbative Gluon pair production from a Constant Chromo-Electric Field via the Schwinger Mechanism in Arbitrary Gauge

We study the non-perturbative production of gluon pairs from a constant SU(3) chromo-electric background field via the Schwinger mechanism. We fix the covariant background gauge with an arbitrary gauge parameter α. We determine the transverse momentum distribution of the gluons, as well as the total probability of creating pairs per unit space time volume. We find that the result is independent of the covariant gauge parameter αused to define arbitrary covariant background gauges. We find that our non-perturbative result is both gauge invariant and gauge parameter αindependent.

hep-ph↗
arXiv2006

Phases of a fermionic model with chiral condensates and Cooper pairs in 1+1 dimensions

We study the phase structure of a 4-fermi model with three bare coupling constants, which potentially has three types of bound states. This model is a generalization of the model discussed previously by A. Chodos et al. [Phys. Rev. D 61, 045011 (2000)], which contained both chiral condensates and Cooper pairs. For this generalization we find that there are two independent renormalized coupling constants which determine the phase structure at finite density and temperature. We find that the vacuum can be in one of three distinct phases depending on the value of these two renormalized coupling constants.

hep-ph↗
arXiv2005

Supersymmetric approximations to the 3D supersymmetric O(N) model

We develop several non-perturbative approximations for studying the dynamics of a supersymmetric O(N) model which preserve supersymmetry. We study the phase structure of the vacuum in both the leading order in large-N approximation as well as in the Hartree approximation, and derive the finite temperature renormalized effective potential. We derive the exact Schwinger-Dyson equations for the superfield Green functions and develop the machinery for going beyond the next to leading order in large-N approximation using a truncation of these equations which can also be derived from a two-particle irreducible effective action.

hep-ph↗
arXiv2005

Spectral correlations of individual quantum graphs

We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $σ$--model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner--Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.

nlin.CD↗
arXiv2005

Renormalized broken-symmetry Schwinger-Dyson equations and the 2PI-1/N expansion for the O(N) model

We derive the renormalized Schwinger-Dyson equations for the one- and two-point functions in the auxiliary field formulation of $λϕ^4$ field theory to order 1/N in the 2PI-1/N expansion. We show that the renormalization of the broken-symmetry theory depends only on the counter terms of the symmetric theory with $ϕ= 0$. We find that the 2PI-1/N expansion violates the Goldstone theorem at order 1/N. In using the O(4) model as a low energy effective field theory of pions to study the time evolution of disoriented chiral condensates one has to {\em{explicitly}} break the O(4) symmetry to give the physical pions a nonzero mass. In this effective theory the {\em additional} small contribution to the pion mass due to the violation of the Goldstone theorem in the 2-PI-1/N equations should be numerically unimportant.

hep-ph↗
arXiv2005

Exact solitary wave solutions for a discrete $λϕ^4$ field theory in 1+1 dimensions

We have found exact, periodic, time-dependent solitary wave solutions of a discrete $ϕ^4$ field theory model. For finite lattices, depending on whether one is considering a repulsive or attractive case, the solutions are either Jacobi elliptic functions $\sn(x,m)$ (which reduce to the kink function $\tanh(x)$ for $m\to 1$), or they are $\dn(x,m)$ and $\cn(x,m)$ (which reduce to the pulse function $\sech(x)$ for $m\to 1$). We have studied the stability of these solutions numerically, and we find that our solutions are linearly stable in most cases. We show that this model is a Hamiltonian system, and that the effective Peierls-Nabarro barrier due to discreteness is zero not only for the two localized modes but even for all three periodic solutions. We also present results of numerical simulations of scattering of kink--anti-kink and pulse--anti-pulse solitary wave solutions.

nlin.SI↗
arXiv2004

SUSY Production From TeV Scale Blackhole at LHC

If the fundamental Planck scale is near a TeV, then we should expect to see TeV scale black holes at the LHC. Similarly, if the scale of supersymmetry breaking is sufficiently low, then we might expect to see light supersymmetric particles in the next generation of colliders. If the mass of the supersymmetric particle is of order a TeV and is comparable to the temperature of a typical TeV scale black hole, then such sparticles will be copiously produced via Hawking radiation: The black hole will act as a resonance for sparticles, among other things. In this paper we compared various signatures for SUSY production at LHC, and we contrasted the situation where the sparticles are produced directly via parton fusion processes with the situation where they are produced indirectly through black hole resonances. We found that black hole resonances provide a larger source for heavy mass SUSY (squark and gluino) production than the direct pQCD-SUSY production via parton fusion processes depending on the values of the Planck mass and blackhole mass. Hence black hole production at LHC may indirectly act as a dominant channel for SUSY production. We also found that the differential cross section dσ/dp_t for SUSY production increases as a function of the p_t (up to p_t equal to about 1 TeV or more) of the SUSY particles (squarks and gluinos), which is in sharp contrast with the pQCD predictions where the differential cross section dσ/dp_t decreases as p_t increases for high p_t about 1 TeV or higher. This is a feature for any particle emission from TeV scale blackhole as long as the temperature of the blackhole is very high (~ TeV). Hence measurement of increase of dσ/dp_t with p_t for p_t up to about 1 TeV or higher for final state particles might be a useful signature for blackhole production at LHC.

hep-ph↗