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Alan Chodos

Publications and source records attributed to Alan Chodos.

At least 19 recordsLinked to original sources
arXiv2025

A Generalized Nonlinear Extension of Quantum Mechanics

We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying Hamiltonian structure. We analyze a particular solution in detail, and we use a natural extension of the Born rule to compute particle trajectories. We find that closed particle orbits are possible.

quant-ph↗
arXiv2024

Geometric Interpretation of a nonlinear extension of Quantum Mechanics

We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. In this paper we suggest that the two components of the wave function represent the system described by the Hamiltonian H in two different asymptotic regions of spacetime and we show that the non-linear terms can be viewed as giving rise to gravitational effects.

quant-ph↗
arXiv2022

A Solvable Model of a Nonlinear extension of Quantum Mechanics

We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We hope that this simple example will elucidate some of the issues of interpreting nonlinear generalization of quantum mechanics that have been put forth to resolve questions about quantum measurement theory.

quant-ph↗
arXiv2022

Tachyons as a Consequence of Light-Cone Reflection Symmetry

We introduce a new symmetry, Light-Cone Reflection (LCR), which interchanges timelike and spacelike intervals. Our motivation is to provide a reason, based on symmetry, why tachyons might exist, with emphasis on application to neutrinos. We show that LCR, combined with translations, leads to a much larger symmetry. We construct an LCR-invariant Lagrangian, and discuss some of its properties. In a simple example, we find complete symmetry in the spectrum between tachyons and ordinary particles. We also show that the theory allows for the introduction of a further gauge invariance related to chiral symmetry.

hep-ph↗
arXiv2020

Neutrino condensation from a New Higgs Interaction

We study the consequences of having a new interaction between neutrinos and a Higgs scalar. We find that there are two possible attractive channels in the resulting effective 4-fermi theory which lead to a neutrino condensation in cosmic neutrinos and the creation of a neutrino superfluid at low temperatures and finite density. We find that at the minimum of the effective potential V the condensates are mostly made up of pairs of left-left+ right-right composites, with a slight admixture of left-right + right-left composites.

hep-ph↗
arXiv2016

Chirally Invariant Avatar in a Model of Neutrinos with Light Cone Reflection Symmetry

In previous work we developed a model of neutrinos based on a new symmetry, Light Cone Reflection (LCR), that interchanges spacelike and timelike intervals. In this paper we start with the four-dimensional model, and construct a two-dimensional avatar that obeys the same equations of motion, and preserves both the light-cone reflection symmetry and the chiral symmetry of the original theory. The avatar also contains the interaction that rendered the four-dimensional model gauge invariant. In an addendum, we make some remarks about how to determine the scalar field that enters into the definition of the LCR-covariant derivative.

hep-ph↗
arXiv2016

Gauge Interactions and a Quantum Avatar in a Model with Light Cone Reflection Symmetry

We continue the development of a model of neutrinos that possesses a new symmetry, Light Cone Reflection, interchanging spacelike and timelike intervals. In this paper we introduce gauge interactions in which only the physical modes of the theory participate. We also find an avatar of the theory, involving spinors in two-dimensions that obey equations reproducing the spectrum of the original, four-dimensional theory, and we discuss the quantization of the avatar.

hep-ph↗
arXiv2015

A Model of Neutrinos

We propose a model for neutrinos based on symmetry under light-cone reflection (LCR), which was introduced in a previous paper. LCR is realized using a minimal substitution, which allows the equations of motion to be solved after a suitable coordinate transformation. Some consequences of this proposal are discussed.

hep-ph↗
arXiv2012

Light Cone Reflection and the Spectrum of Neutrinos

We extend the treatment of neutrinos within the context of SIM(2) Very Special Relativity (VSR) by adding a new discrete symmetry that we call Light Cone Reflection (LCR). We construct a Lagrangian that exhibits both VSR and LCR symmetry, and find that the spectrum involves two neutrinos, one tachyonic and the other not, with the same absolute value of the mass parameter. We argue that LCR symmetry offers a rationale for introducing tachyonic neutrinos.

hep-ph↗
arXiv2003

An O(N) symmetric extension of the Sine-Gordon Equation

We discuss an O(N) exension of the Sine-Gordon (S-G)equation which allows us to perform an expansion around the leading order in large-N result using Path-Integral methods. In leading order we show our methods agree with the results of a variational calculation at large-N. We discuss the striking differences for a non-polynomial interaction between the form for the effective potential in the Gaussian approximation that one obtains at large-N when compared to the N=1 case. This is in contrast to the case when the classical potential is a polynomial in the field and no such drastic differences occur. We find for our large-N extension of the Sine-Gordon model that the unbroken ground state is unstable as one increases the coupling constant (as it is for the original S-G equation) and we determine the stability criteria.

hep-th↗
arXiv2000

Nonsingular deformations of singular compactifications, the cosmological constant, and the hierarchy problem

We consider deformations of the singular "global cosmic string" compactifications, known to naturally generate exponentially large scales. The deformations are obtained by allowing a constant curvature metric on the brane and correspond to a choice of integration constant. We show that there exists a unique value of the integration constant that gives rise to a nonsingular solution. The metric on the brane is dS_4 with an exponentially small value of expansion parameter. We derive an upper bound on the brane cosmological constant. We find and investigate more general singular solutions---``dilatonic global string" compactifications---and show that they can have nonsingular deformations. We give an embedding of these solutions in type IIB supergravity. There is only one class of supersymmetry-preserving singular dilatonic solutions. We show that they do not have nonsingular deformations of the type considered here.

hep-th↗
arXiv2000

Dynamics of the chiral phase transition at finite chemical potential

We study the dynamics of the chiral phase transition at finite chemical potential in the Gross-Neveu model in the leading order in large-N approximation. We consider evolutions starting in local thermal equilibrium in the massless unbroken phase for conditions pertaining to traversing a first or second order phase transition. We assume boost invariant kinematics and determine the evolution of the the order parameter $\sigma$, the energy density and pressure as well as the effective temperature, chemical potential and interpolating number densities as a function of $\tau$.

hep-ph↗
arXiv1999

Warp Factors and Extended Sources in Two Transverse Dimensions

We study the solutions of the Einstein equations in (d+2)-dimensions, describing parallel p-branes (p=d-1) in a space with two transverse dimensions of positive gaussian curvature. These solutions generalize the solutions of Deser and Jackiw of point particle sources in (2+1)-dimensional gravity with cosmological constant. Determination of the metric is reduced to finding the roots of a simple algebraic equation. These roots also determine the nontrivial "warp factors" of the metric at the positions of the branes. We discuss the possible role of these solutions and the importance of "warp factors" in the context of the large extra dimensions scenario.

hep-th↗
arXiv1999

A Two-dimensional Model with Chiral Condensates and Cooper Pairs having QCD-like Phase Structure

We generalize our previous model to an O(N) symmetric two-dimensional model which possesses chiral symmetry breaking and superconducting (Cooper pair condensates) phases at large-N. At zero temperature and density, the model can be solved analytically in the large-N limit. We perform the renormalization explicitly and obtain a closed form expression of the effective potential. There exists a renormalization group invariant parameter $δ$ that determines which of the condensates exist in the vacuum. At finite temperatures and densities, we map out the phase structure of the model by a detailed numerical analysis of the renormalized effective potential. For $δ$ positive and sufficiently large, the phase diagram in the $μ$-$T$ (chemical potential-temperature) plane exactly mimics the features expected for QCD with two light flavors of quarks. At low temperatures there exists low-$μ$ chiral symmetry breaking and high-$μ$ Cooper pair condensate regions which are separated by a first-order phase transition. At high $μ$, when the temperature is raised, the system undergoes a second-order phase transition from the superconducting phase to an unbroken phase in which both condensates vanish. For a range of values of $δ$ the theory possesses a tricritical point ($μ_{tc}$ and $T_{tc}$); for $μ> μ_{tc}$ ($μ< μ_{tc}$) the phase transition from the low temperature chiral symmetry breaking phase to unbroken phase is first-order (second-order). For the range of $δ$ in which the system mimics QCD, we expect the model to be useful for the investigation of dynamical aspects of nonequilibrium phase transitions, and to provide information relevant to the study of relativistic heavy ion collisions and the dense interiors of neutron stars.

hep-ph↗
arXiv1999

Concatenation of Scales Below 1 eV

There are (at least) four numbers of physical and cosmological significance whose inferred values, when expressed in mass units, cluster in a window below 1 eV. These are: the neutrino mass, the neutrino chemical potential, the cosmological constant, and the size of two extra dimensions (if the fundamental scale of gravity is 1-10 TeV). In this note, we imagine ways in which these four numbers could all be connected.

hep-ph↗
arXiv1999

Competing Condensates in Two Dimensions

We generalize our previous 2-dimensional model in which a pairing condensate psi-psi was generated at large N. In the present case, we allow for both psi-psi and a chiral condensate psibar-psi to exist. We construct the effective potential to leading order in 1/N, and derive the gap equations at finite density and temperature. We study the zero density and temperature situation analytically. We perform the renormalization explicitly and we show that the physics is controlled by a parameter related to the relative strengths of the interactions in the pairing and chiral channels. We show that although a solution to the gap equations exists in which both condensates are non-vanishing, the global minimum of the effective potential always occurs for the case when one or the other condensate vanishes.

hep-ph↗