On a numerical exact solution to the many-body problem in one dimension

Pauli, Hans–Christian

doi:10.1007/bf01412544

Cited by 9 publications

(13 citation statements)

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“…Most of its statelets will not exhibit a vanishing excitation number, yet the state as a whole is more symmetric than the generic four-parton eigenstate. To wit, it possesses an additional Z 2 symmetry, 13 so that the 24 independent statelets can be cast into 12 sinusoidal functions, or into the 6 double-sines of Eq. (4.13) in Ref.…”

Section: Applications a Using "Elcq": Some Suggestionsmentioning

confidence: 99%

“…So we are left with two integrations over a trigonometric function divided by a quadratic function of the momenta. The structure of the final expression is therefore 13 Its identity and S 1 statelets fulfill T Zjri ¼ Zjri, whereas for the S 2 statelets we have C 2 jri ¼ Ijri, so that half the statelets are redundant. 14 Note that this works in the massless joeoeoi sector, too.…”

Section: B the Role Of Pair Productionmentioning

confidence: 99%

“…The hospitality of the Ohio State University's Physics Department, where most of this work was completed, is gratefully acknowledged. I would also like to acknowledge the late Hans-Christian Pauli whose work, starting with [13], inspired the method of exhaustive symmetrization developed in this paper.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…This is akin to the DLCQ ansatz which was shown in Ref. [13] to decouple the center of mass motion of a system from its more interesting physics.…”

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confidence: 98%

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A harmonic solution for two-dimensional adjoint QCD

Trittmann

2018

Phys. Rev. D

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Two-dimensional QCD with adjoint fermions has many attractive features, yet its single-particle content remains largely unknown. To lay the foundation for a crucially improved approximation of the theory's spectrum, we developed a method to find the basis of eigenstates using the symmetry structure of the asymptotic theory where pair production is disallowed. This method produces complete sets of multidimensional harmonic functions for the massless and the massive theory. Previously only part of such a basis was known. The method presented here should be applicable to other theories and has the promise of factoring out the long-range Coulomb-type part of interactions. The role of pair production and implications for the bosonized theory in the case of adjoint QCD 2 are discussed.

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Section: Applications a Using "Elcq": Some Suggestionsmentioning

confidence: 99%

Section: B the Role Of Pair Productionmentioning

confidence: 99%

Section: Acknowledgmentsmentioning

confidence: 99%

“…This is akin to the DLCQ ansatz which was shown in Ref. [13] to decouple the center of mass motion of a system from its more interesting physics.…”

mentioning

confidence: 98%

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A harmonic solution for two-dimensional adjoint QCD

Trittmann

2018

Phys. Rev. D

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“…This procedure was actually carried out in one space dimension [15] with two different sets of single-particle functions,…”

Section: The Non-relativistic A-body Problem In One Dimensionmentioning

confidence: 99%

Discretized light-cone quantization and the effective interaction in hadrons

Pauli¹

1999

AIP Conference Proceedings

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Light-cone quantization of gauge theories is discussed from two perspectives: as a calculational tool for representing hadrons as QCD bound-states of relativistic quarks and gluons, and as a novel method for simulating quantum field theory on a computer. A general non-perturbative method for numerically solving quantum field theories, 'discretized light-cone quantization', is outlined. Both the bound-state spectrum and the corresponding relativistic wavefunctions can be obtained by matrix diagonalization and related techniques. Emphasis is put on the construction of the light-cone Fock basis and on how to reduce the many-body problem to an effective Hamiltonian. The usual divergences are avoided by cut-offs and subsequently removed by the renormalization group. For the first time, this programme is carried out within a Hamiltonian approach, from the beginning to the end. Starting with the QCD-Lagrangian, a regularized effective interaction is derived and renormalized, ending up with an almost solvable integral equation. Its eigenvalues yield the mass spectrum of physical mesons, its eigenfunctions yield their wavefunctions including the higher Fock-space components. An approximate but analytic mass formula is derived for all physical mesons.

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Discretized Light-Cone Quantization

Pauli

1996

Neutrino Mass, Dark Matter, Gravitational Waves, Monopole Condensation, and Light Cone Quantization

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The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions is mapped on an effective Hamiltonian which acts only in the Fock space of one quark and one antiquark. The approach is non-perturbative and exact. It is based on Discretized Light-Cone Quantization and the Method of Iterated Resolvents. The method resums the diagrams of perturbation theory to all orders in the coupling constant and is free of Tamm-Dancoff truncations in the Fock-space. Emphasis is put on dealing accurately with the many-body aspects of gauge field theory. Pending future renormalization group analysis the running coupling is derived to all orders in the bare coupling constant. -The derived effective interaction has an amazingly simple structure and is gauge invariant and frame independent. It is solvable on a small computer like a work station. The many-body amplitudes can be retrieved selfconsistently from these solutions, by quadratures without solving another eigenvalue problem. The structures found allow also for developing simple phenomenological models consistent with non-Abelian gauge field theory.

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On a numerical exact solution to the many-body problem in one dimension

Cited by 9 publications

References 13 publications

A harmonic solution for two-dimensional adjoint QCD

A harmonic solution for two-dimensional adjoint QCD

Discretized light-cone quantization and the effective interaction in hadrons

Discretized Light-Cone Quantization

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