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O. W. Greenberg

Publications and source records attributed to O. W. Greenberg.

At least 19 recordsLinked to original sources
arXiv2013

N-quantum calculation of the hydrogen atom with one-photon exchange

The N-quantum approach (NQA) to quantum field theory uses the complete and irreducible set of in or out fields, including in or out fields for bound states, as standard building blocks to construct solutions to quantum field theories. In particular, introducing in (or out) fields for the bound states allows a new way to calculate energy levels and wave functions for the bound states that is both covariant and effectively 3-dimensional. This method is independent of the Bethe-Salpeter equation. In contrast to the Bethe-Salpeter equation, all solutions of the NQA are normalizable and correspond to physical bound states. In this paper we use the NQA in one-loop approximation to calculate states of the relativistic hydrogen atom and analogous two-body systems to illustrate how our new method works. With additional terms in the in field expansion we find systematic corrections beyond the Coulomb interaction.

quant-ph↗
arXiv2012

Construction of asymptotic fields for a charged particle

Asymptotic fields do not exist in theories with massless particles and fields, because the vacuum matrix elements of products of the interacting fields in such theories do not have delta function or principal value singularities in momentum space. We remedy this problem by constructing a field for the charged particle that does have the required singularities in momentum space. We illustrate this construction in quantum electrodynamics (QED).

hep-ph↗
arXiv2011

Remarks on a challenge to the relation between $CPT$ and Lorentz violation

The objection [arXiv:1103.0168] to my theorem [arXiv:hep-ph/0201258] that violation of $CPT$ symmetry implies violation of Lorentz covariance is based on a nonlocal model in which time-ordered products are not well defined. I used covariance of time-ordered products as the condition for Lorentz covariance; therefore the proposed objection is not relevant to my result.

hep-ph↗
arXiv2011

Quarks and quantum statistics

I write about Héctor, his contributions to the early work in the quark model, and a general discussion of quantum statistics

physics.hist-ph↗
arXiv2010

Review of the N-quantum Approach to Bound States

We describe a method of solving quantum field theories using operator techniques based on the expansion of interacting fields in terms of asymptotic fields. For bound states, we introduce an asymptotic field for each (stable) bound state. We choose the nonrelativistic hydrogen atom as an example to illustrate the method. Future work will apply this N-quantum approach to relativistic theories that include bound states in motion.

hep-th↗
arXiv2008

Generalizations of quantum statistics

We review generalizations of quantum statistics, including parabose, parafermi, and quon statistics, but not including anyon statistics, which is special to two dimensions.

quant-ph↗
arXiv2006

Schematic model of generations

We propose a model of generations that has exactly three generations. This model has several attractive features: There is a simple mechanism to produce the CKM quark mixings and their neutrino analogs. There are definite predictions for particles of much higher mass than the quarks and leptons of the standard model, including the prediction of two-body decays without missing mass for the higher mass particles. There is a natural dark matter particle. A discussion of masses of the quarks suggests that the large mass differences between the generations could have a qualitative explanation, and there could be a simple way to make the $u$-$d$ mass difference negative, but the $c$-$s$ and $t$-$b$ mass differences positive. The model also suggests a completely new scenario for the production, mass and decays of the Higgs meson that will be analysed in a separate paper.

hep-ph↗
arXiv2006

Covariance of Time-Ordered Products Implies Local Commutativity of Fields

We formulate Lorentz covariance of a quantum field theory in terms of covariance of time-ordered products (or other Green's functions). This formulation of Lorentz covariance implies spacelike local commutativity or anticommutativity of fields, sometimes called microscopic causality or microcausality. With this formulation microcausality does not have to be taken as a separate assumption.

hep-th↗
arXiv2005

Failure of microcausality in quantum field theory on noncommutative spacetime

The star commutator of $:ϕ(x) \star ϕ(x):$ with $:ϕ(y) \star ϕ(y):$ fails to vanish at equal times and thus also fails to obey microcausality at spacelike separation even for the case in which $θ^{0i}=0$. The failure to obey microcausality for this sample observable implies that this form of noncommutative field theory fails to obey microcausality in general. This result also holds for general fields and observables. We discuss possible responses to this problem.

hep-th↗
arXiv2004

Path Integrals for Parastatistics

We demonstrate that parastatistics can be quantized using path integrals by calculating the generating functionals for time-ordered products of both free and interacting parabose and parafermi fields in terms of path integrals. We also give a convenient form of the commutation relations for the Green components of the parabose and parafermi operators in both the canonical and path integral formalisms.

math-ph↗
arXiv2003

Why is CPT fundamental?

G. Lüders and W. Pauli proved the $\mathcal{CPT}$ theorem based on Lagrangian quantum field theory almost half a century ago. R. Jost gave a more general proof based on ``axiomatic'' field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why $\mathcal{CPT}$ is fundamental--because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the $\mathcal{CPT}$ transform of any relativistic field without calculating $\mathcal{C}$, $\mathcal{P}$ and $\mathcal{T}$ separately and then multiplying them. The purpose of this pedagogical paper is to ``deaxiomatize'' the $\mathcal{CPT}$ theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary.

hep-ph↗
arXiv2003

Hybrid Dirac Fields

Hybrid Dirac fields are fields that are general superpositions of the annihilation and creation parts of four Dirac spin 1/2 fields, $ψ^{(\pm)}(x;\pm m)$, whose annihilation and creation parts obey the Dirac equation with mass $m$ and mass $-m$. We discuss a specific case of such fields, which has been called ``homeotic.'' We show for this case, as is true in general for hybrid Dirac fields (except the ordinary fields whose annihilation and creation parts both obey one or the other Dirac equation), that (1) any interacting theory violates both Lorentz covariance and causality, (2) the discrete transformations $\mathcal{C}$, and $\mathcal{CPT}$ map the pair $ψ_h(x)$ and $\barψ_h(x)$ into fields that are not linear combinations of this pair, and (3) the chiral projections of $ψ_h(x)$ are sums of the usual Dirac fields with masses $m$ and $-m$; on these chiral projections $\mathcal{C}$, and $\mathcal{CPT}$ are defined in the usual way, their interactions do not violate $\mathcal{CPT}$, and interactions of chiral projections are Lorentz covariant and causal. In short, the main claims concerning ``homeotic'' fields are incorrect.

hep-ph↗
arXiv2002

From Wigner's Supermultiplet Theory to Quantum Chromodynamics

The breadth of Eugene Wigner's interests and contributions is amazing and humbling. At different times in his life he did seminal work in areas as diverse as pure mathematics and chemical engineering. His seminal research in physics is, of course, the best known. In this talk I first describe Wigner's supermultiplet theory of 1936 using the approximate symmetry of the nuclear Hamiltonian under a combined spin-isospin symmetry to describe the spectroscopy of stable nuclei up to about the nucleus molybdenum. I then show how Wigner's ideas of 1936 have had far reaching and unexpected implications: his ideas led to the discovery of the color degree of freedom for quarks and to the symmetric quark model of baryons which is the basis of baryon spectroscopy. I conclude by pointing out that the color degree of freedom, made into a local symmetry using Yang-Mills theory, leads to the gauge theory of color, quantum chromodynamics, which is our present theory of the strong interactions.

hep-ph↗
arXiv2002

CPT Violation Implies Violation of Lorentz Invariance

An interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.

hep-ph↗