Uniform acceleration and the quantum field theory vacuum,I

Free massless scalar and Dirac fields are quantized in two-dimensional Minkowski space in a representation in which the energy operator for a uniformly accelerating observer is diagonalized. The usual vacuum, and many other pure states, appear to be thermally excited in this representation. The crucial role ot PCT symmetry, as regards the general validity of this conclusion, is illustrated.     

Topological quantum field theory

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The model may also be interesting from a physical viewpoint; it is in a sense a generally covariant quantum field theory, albeit one in which general covariance is unbroken, there are no gravitons, and the only excitations are topological.On leave from Department of Physics, Princeton University. Research supported in part by NSF Grants No. 80-19754, 86-16129, 86-20266     

Hyperfunction quantum field theory

The quantum field theory in terms of Fourier hyperfunctions is constructed. The test function space for hyperfunctions does not containC functions with compact support. In spite of this defect the support concept ofH-valued Fourier hyperfunctions allows to formulate the locality axiom for hyperfunction quantum field theory.     

Quaternionic quantum field theory

We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second order wave equation. The theory takes the form of either a functional integral with quaternion-imaginary Lagrangian, or a Schrödinger equation and transformation theory for quaternion-valued wave functions, with a quaternion-imaginary Hamiltonian. The connection between the two formulations is developed in detail, and many related issues, including the breakdown of the correspondence principle and the Hilbert space structure, are discussed.     

Point-form quantum field theory

We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form x_μx^μ = τ². This choice of quantization surface implies that all components of the 4-momentum operator are affected by interactions (if present), whereas rotation and boost generators remain interaction free—a feature characteristic of Dirac’s “point-form” of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincaré generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.     

The Boltzmann equation from quantum field theory

We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff–Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff–Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.     

The origin of three-cocycles in quantum field theory

When quantising a classical field theory it is not automatic that a group of symmetries of the classical system is preserved as a symmetry of the quantum system. Apart from the phenomenon of symmetry breaking it can also happen (as in Faddeev's Gauss law anomaly) that only an extension of the classical group acts as a symmetry group of the quantum system. We show here that rather than signalling a failure of the associative law as has been suggested in the literature, the occurrence of a non-trivial three-cocycle on the local gauge group is an “anomaly” or obstruction to the existence of an extension of the local gauge group acting as a symmetry group of the quantum system.     

The spontaneously broken supersymmetry in quantum field theory

It is shown that every spontaneous breaking of supersymmetry can be accomplished by means of a locally conserved supercurrent

$\text{εαβf}{}^{\mathrm{+}}{}_{\mathrm{<mtext>\gamma </mtext><mtext>?</mtext>}}\text{, α, β, γ = 1, 2,}$

$\text{εαβ =}\text{0}\text{1}\text{?1}\text{1}$

, where $\text{f}{}^{\mathrm{+}}{}_{\mathrm{<mtext>\gamma </mtext><mtext>?</mtext>}}$ is a massless field satisfying the Weyl Equation. For a given supercurrent $\text{jαβ}\text{γ}\text{?}$ the necessary condition that it will break spontaneously the supersymmetry is

$\text{jαβ}\text{γ}\text{?}\text{?jβα}\text{γ}\text{?}\text{≠0.}$

It is shown that the anticommutation relations of the broken supercharges are not related to the energy-momentum vector.Similar procedure applied in case of a vector field is inconclusive.The extension of the Maisson and Reeh statement on the helicity of Goldstone fields is given.     

The entropy bound for local quantum field theory

We investigate the entropy bound for local quantum field theory in this Letter. Both the bosonic and fermionic fields confined to an asymptotically flat space–time are examined. By imposing the non-gravitational collapse condition, we find both of them are limited by the same entropy bound A3/4$A^{3/4}$, where A is the boundary area of the region where the quantum fields are contained in. The gap between this entropy bound and the holographic entropy has been verified.     

The Heisenberg ferromagnet as a quantum field theory

We consider a lattice of spin 1/2 ions, described by the discrete form of the current commutation relationsJ _i J _(i) =1/2, [J _i ,J _i ]=i _ij J _i where =1, 2, 3 andi label the lattice sites. The algebra is realized as the Clifford algebra over a Hilbert space. The equations of motion are specified by a formal Hamiltonian of the Heisenberg form: , wheref _ij 0 and only a finite numberQ of ions are linked to any given lattice site. We prove that the Hamiltonian is non-negative in a representation of , and has a ground state exhibiting ferromagnetism. The time displacement group acts continuously on , inducing automorphisms. is asymptotically abelian with respect to the space translations of the lattice.The model is an example of an algebraic quantum field theory and possesses a broken symmetry, the rotation group 0(3). The consequent Goldstone theorem is proved, namely, there is no energy gap in the spectrum ofH.     

量子场论方法在电子与分子碰撞中的应用

这是一种利用量子场论所进行的探究性的研究方法,在文章中,我们设 计了一种新的较为简单的电子-原子碰撞模型,将量子场论方法与光学势方法中的可加性规 则结合起来.利用这种模型,我们计算了e-H,e-He和e-Li的微分碰撞截面,获得了较满意的 结果.     

The star product in interacting quantum field theory

Letters in Mathematical Physics - We propose a new formula for the star product in deformation quantization of Poisson structures related in a specific way to a variational problem for a function...     

Zitterbewegung in quantum field theory

Traditionally, the zitterbewegung （ZB） of the Dirac electron has just been studied at the level of quantum mechanics. Seeing the fact that an old interest in ZB has recently been rekindled by the investigations on spintronic, graphene, and superconducting systems, etc., this paper presents a quantum-field-theory investigation on ZB and obtains the conclusion that, the ZB of an electron arises from the influence of virtual electron-positron pairs （or vacuum fluctuations） on the electron.     

Two-dimensional conformal quantum field theory

On leave of absence from the Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria.     

Renormalizable noncommutative quantum field theory

We discuss the Euclidean noncommutative f⁴₄{\phi^4_4}-quantum field theory as an example of a renormalizable field theory. Using a Ward identity, Disertori, Gurau, Magnen and Rivasseau were able to prove the vanishing of the beta function for the coupling constant to all orders in perturbation theory. We extend this work and obtain from the Schwinger–Dyson equation a non-linear integral equation for the renormalised two-point function alone. The non-trivial renormalised four-point function fulfils a linear integral equation with the inhomogeneity determined by the two-point function. These integral equations might be the starting point of a nonperturbative construction of a Euclidean quantum field theory on a noncommutative space. We expect to learn about renormalisation from this almost solvable model.     

Duality in quantum field theory

We postulate a convergent version of operator product expansions on the vacuum and explore some of their consequences. They lead to structures much reminiscent of dual resonance models.     

Noncommutative quantum mechanics from noncommutative quantum field theory

We derive noncommutative multiparticle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Particles of opposite charges are found to have opposite noncommutativity. As a result, there is no noncommutative correction to the hydrogen atom spectrum at the tree level. We also comment on the obstacles to take noncommutative phenomenology seriously and propose a way to construct noncommutative SU(5) grand unified theory.     

The significance of conformal inversion in quantum field theory

The 2-point functions of Euclidean conformal invariant quantum field theory are looked at as intertwining kernels of the conformal group. In this analysis a fundamental role is played by a two-element groupW, whose non-identity element =R·I consists of the conformal inversionR multiplied by a space-time reflectionI. The propagators of conformal invariant quantum field theory are determined by the requirement of -covariance. The importance of the -inversion in the theory of Zeta-functions is mentioned.