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J. R. Hiller

Publications and source records attributed to J. R. Hiller.

72 records · Page 4Linked to original sources
arXiv2001

Exact solutions to Pauli-Villars-regulated field theories

We present a new class of quantum field theories which are exactly solvable. The theories are generated by introducing Pauli-Villars fermionic and bosonic fields with masses degenerate with the physical positive metric fields. An algorithm is given to compute the spectrum and corresponding eigensolutions. We also give the operator solution for a particular case and use it to illustrate some of the tenets of light-cone quantization. Since the solutions of the solvable theory contain ghost quanta, these theories are unphysical. However, we also discuss how perturbation theory in the difference between the masses of the physical and Pauli-Villars particles could be developed, thus generating physical theories. The existence of explicit solutions of the solvable theory also allows one to study the relationship between the equal-time and light-cone vacua and eigensolutions.

hep-th↗
arXiv2001

Application of Pauli-Villars regularization and discretized light-cone quantization to a single-fermion truncation of Yukawa theory

We apply Pauli-Villars regularization and discretized light-cone quantization to the nonperturbative solution of (3+1)-dimensional Yukawa theory in a single-fermion truncation. Three heavy scalars, including two with negative norm, are used to regulate the theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of a new, indefinite-metric Lanczos algorithm. Various observables are extracted from the wave functions, including average multiplicities and average momenta of constituents, structure functions, and a form factor slope.

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arXiv2001

Perturbative QCD and factorization of coherent pion photoproduction on the deuteron

We analyze the predictions of perturbative QCD for pion photoproduction on the deuteron, gamma D -> pi^0 D, at large momentum transfer using the reduced amplitude formalism. The cluster decomposition of the deuteron wave function at small binding only allows the nuclear coherent process to proceed if each nucleon absorbs an equal fraction of the overall momentum transfer. Furthermore, each nucleon must scatter while remaining close to its mass shell. Thus the nuclear photoproduction amplitude, M_{gamma D -> pi^0 D}(u,t), factorizes as a product of three factors: (1) the nucleon photoproduction amplitude, M_{gamma N_1 -> pi^0 N_1}(u/4,t/4), at half of the overall momentum transfer, (2) a nucleon form factor, F_{N_2}(t/4), at half the overall momentum transfer, and (3) the reduced deuteron form factor, f_d(t), which according to perturbative QCD, has the same monopole falloff as a meson form factor. A comparison with the recent JLAB data for gamma D -> pi^0 D of Meekins et al. [Phys. Rev. C 60, 052201 (1999)] and the available gamma p -> pi^0 p data shows good agreement between the perturbative QCD prediction and experiment over a large range of momentum transfers and center of mass angles. The reduced amplitude prediction is consistent with the constituent counting rule, p^11_T M_{gamma D -> pi^0 D} -> F(theta_cm), at large momentum transfer. This is found to be consistent with measurements for photon lab energies E_gamma > 3 GeV at theta_cm=90 degrees and $\elab > 10$ GeV at 136 degrees.

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arXiv2001

Wave functions and properties of massive states in three-dimensional supersymmetric Yang-Mills theory

We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric Yang-Mills theory on R x S^1 x S^1. One of the compact directions is chosen to be light-like and the other to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound-state wave functions and masses numerically without renormalizing. We present an overview of all the massive states of this theory, and we see that the spectrum divides into two distinct and disjoint sectors. In one sector the SDLCQ approximation is only valid up to intermediate coupling. There we find a well defined and well behaved set of states, and we present a detailed analysis of these states and their properties. In the other sector, which contains a completely different set of states, we present a much more limited analysis for strong coupling only. We find that, while these state have a well defined spectrum, their masses grow with the transverse momentum cutoff. We present an overview of these states and their properties.

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arXiv2001

Field Theory Correlators and String Theory

It appears that string-M-theory is the only viable candidate for a complete theory of matter. It must therefore contain both gravity and QCD. What is particularly surprising is the recent conjecture that strongly coupled QCD matrix elements can be evaluated though a duality with weakly coupled gravity. To date there has been no direct verification of this conjecture by Maldacena because of the difficulty of direct strong coupling calculations in gauge theories. We report here on some progress in evaluating a gauge-invariant correlator in the non-perturbative regime in two and three dimensions in SYM theories. The calculations are made using supersymmetric discrete light-cone quantization (SDLCQ). We consider a Maldacena-type conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation, solve the corresponding N=(8,8) SYM theory in two dimensions, and evaluate the correlator of the stress-energy tensor. Our numerical results support the Maldacena conjecture and are within 10-15% of the predicted results. We also present a calculation of the stress-energy correlator in N=1 SYM theory in 2+1 dimensions. While there is no known duality relatingthis theory to supergravity, the theory does have massless BPS states, and the correlator gives important information about the BPS wave function in the non-perturbative regime.

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arXiv2001

Two-Point Stress-Tensor Correlator in N=1 SYM(2+1)

Recent advances in string theory have highlighted the need for reliable numerical methods to calculate correlators at strong coupling in supersymmetric theories. We present a calculation of the correlator <0|T^{++}(r)T^{++}(0)|0> in N=1 SYM theory in 2+1 dimensions. The numerical method we use is supersymmetric discrete light-cone quantization (SDLCQ), which preserves the supersymmetry at every order of the approximation and treats fermions and bosons on the same footing. This calculation is done at large $N_c$. For small and intermediate r the correlator converges rapidly for all couplings. At small r the correlator behaves like 1/r^6, as expected from conformal field theory. At large r the correlator is dominated by the BPS states of the theory. There is, however, a critical value of the coupling where the large-r correlator goes to zero, suggesting that the large-r correlator can only be trusted to some finite coupling which depends on the transverse resolution. We find that this critical coupling grows linearly with the square root of the transverse momentum resolution.

hep-th↗
arXiv2000

Application of Discrete Light-Cone Quantization to Yukawa Theory in Four Dimensions

The numerical technique of discrete light-cone quantization (DLCQ) is applied to a single-fermion truncation of Yukawa theory in four dimensions. The truncated theory is regulated by three Pauli-Villars bosons, which are introduced directly in the DLCQ Fock-state basis. A special form of the Lanczos diagonalization algorithm is used to handle the indefinite metric. Renormalization is done nonperturbatively.

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arXiv2000

Calculations with DLCQ

The method of discrete light-cone quantization (DLCQ) and useful refinements are summarized. Applications to various field theories are reviewed.

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arXiv2000

Methods for the nonperturbative approximation of form factors and scattering amplitudes

Methods are described for the nonperturbative calculation of wave functions and scattering amplitudes in light-cone quantization. Form factors are computed from the boost-invariant wave functions, which appear as coefficients in a Fock-state expansion of the field-theoretic eigenstate. A technique is proposed for calculating scattering amplitudes from matrix elements of a T operator between such composite-particle eigenstates.

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arXiv2000

Nonperturbative Calculation of Scattering Amplitudes

A method for the nonperturbative calculation of scattering amplitudes and cross sections is discussed in the context of light-cone quantization. The Lanczos-based recursion method of Haydock is suggested for the computation of matrix elements of the resolvent for the light-cone Hamiltonian, from which the T-matrix can be constructed. The scattering of composite particles is handled by a generalization of a formulation given by Wick.

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arXiv2000

Towards a SDLCQ test of the Maldacena Conjecture

We consider the Maldacena conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation and present numerical results of a test of the conjecture against the boundary field theory calculation using DLCQ. We previously calculated the two-point function of the stress-energy tensor on the supergravity side; the methods of Gubser, Klebanov, Polyakov, and Witten were used. On the field theory side, we derived an explicit expression for the two-point function in terms of data that may be extracted from the supersymmetric discrete light cone quantization (SDLCQ) calculation at a given harmonic resolution. This yielded a well defined numerical algorithm for computing the two-point function. For the supersymmetric Yang-Mills theory with 16 supercharges that arises in the Maldacena conjecture, the algorithm is perfectly well defined; however, the size of the numerical computation prevented us from obtaining a numerical check of the conjecture. We now present numerical results with approximately 1000 times as many states as we previously considered. These results support the Maldacena conjecture and are within $10-15%$ of the predicted numerical results in some regions. Our results are still not sufficient to demonstrate convergence, and, therefore, cannot be considered to a numerical proof of the conjecture. We present a method for using a ``flavor'' symmetry to greatly reduce the size of the basis and discuss a numerical method that we use which is particularly well suited for this type of matrix element calculation.

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arXiv1999

On the Use of Discrete Light-Cone Quantization to Compute Form Factors

Techniques for the field-theoretic calculation of a form factor are described and applied to a dressed-fermion state of a (3+1)-dimensional model Hamiltonian. Discrete light-cone quantization plays the crucial role as the means by which Fock-state wave functions are computed. An ultraviolet infinity is controlled by Pauli-Villars regularization.

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arXiv1999

Pauli-Villars regularization in DLCQ

Calculations in a (3+1)-dimensional model indicate that Pauli-Villars regularization can be combined with discrete light-cone quantization (DLCQ) to solve at least some field theories nonperturbatively. Discrete momentum states of Pauli-Villars particles are included in the Fock basis to automatically generate needed counterterms; the resultant increase in basis size is found acceptable. The Lanczos algorithm is used to extract the lowest massive eigenstate and eigenvalue of the light-cone Hamiltonian, with basis sizes ranging up to 10.5 million. Each Fock-sector wave function is computed in this way, and from these one can obtain values for various quantities, such as average multiplicities and average momenta of constituents, structure functions, and a form-factor slope.

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arXiv1998

Pauli-Villars Regularization in a Discrete Light-Cone Model

Pauli-Villars regularization is successfully applied to nonperturbative calculations in a (3+1)-dimensional light-cone model. Numerical results obtained with discretized light-cone quantization compare favorably with the analytic solution.

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arXiv1998

Pauli--Villars as a Nonperturbative Ultraviolet Regulator in Discretized Light-Cone Quantization

We propose a solution to the problem of renormalizing light-cone Hamiltonian theories while maintaining Lorentz invariance and other symmetries. The method uses generalized Pauli--Villars regulators to render the theory finite. We discuss the method in the context of Yukawa theory at one loop and for a soluble model in 3+1 dimensions. The model is studied nonperturbatively. Numerical results obtained with use of discretized light-cone quantization, special integration weighting factors, and the complex symmetric Lanczos diagonalization algorithm compare well with the analytic answers.

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arXiv1997

Nonperturbative Renormalization in Light-Cone Quantization

Two approaches to nonperturbative renormalization are discussed for theories quantized on the light cone. One is tailored specifically to a calculation of the dressed-electron state in quantum electrodynamics, where an invariant-mass cutoff is used as a regulator and a Tamm-Dancoff truncation is made to include no more than two photons. The other approach is based on Pauli-Villars regulators and is applied to Yukawa theory and a related soluble model. In both cases discretized light-cone quantization is used to obtain a finite matrix problem that can be solved nonperturbatively.

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arXiv1996

Nonperturbative Renormalization of QED in Light-Cone Quantization

As a precursor to work on QCD, we study the dressed electron in QED nonperturbatively. The calculational scheme uses an invariant mass cutoff, discretized light-cone quantization, a Tamm--Dancoff truncation of the Fock space, and a small photon mass. Nonperturbative renormalization of the coupling and electron mass is developed.

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