arXiv subjects
Publications and source records attributed to Stephen L. Adler.
We give a detailed analysis of the anti-self-adjoint operator contribution to the fluctuation terms in the trace dynamics Ward identity. This clarifies the origin of the apparent inconsistency between two forms of this identity discussed in Chapter 6 of our recent book on emergent quantum theory.
These are the commentaries for a volume of reprints of my selected papers with commentaries that I am preparing for publication by World Scientific. Contents: Preface; (1)Early Years, and Condensed Matter Physics; (2) High Energy Neutrino Reactions, PCAC Relations, and Sum Rules; (3) Anomalies: Chiral Anomalies and Their Nonrenormalization, Perturbative Corrections to Scaling, and Trace Anomalies to All Orders; (4) Quantum Electrodynamics; (5) Particle Phenomenology and Neutral Currents; (6) Gravitation; (7) Non-Abelian Monopoles, Confinement Models, and Chiral Symmetry Breaking; (8) Overrelaxation for Monte-Carlo and Other Algorithms; (9) Quaternionic Quantum Mechanics, Trace Dynamics, and Emergent Quantum Theory; (10) Where Next?
Careful monitoring of harmonically bound (or as a limiting case, free) masses is the basis of current and future gravitational wave detectors, and of nanomechanical devices designed to access the quantum regime. We analyze the effects of stochastic localization models for state vector reduction, and of related models for environmental decoherence, on such systems, focusing our analysis on the non-dissipative forced harmonic oscillator, and its free mass limit. We derive an explicit formula for the time evolution of the expectation of a general operator in the presence of stochastic reduction or environmentally induced decoherence, for both the non-dissipative harmonic oscillator and the free mass. In the case of the oscillator, we also give a formula for the time evolution of the matrix element of the stochastic expectation density matrix between general coherent states. We show that the stochastic expectation of the variance of a Hermitian operator in any unraveling of the stochastic process is bounded by the variance computed from the stochastic expectation of the density matrix, and we develop a formal perturbation theory for calculating expectation values of operators within any unraveling. Applying our results to current gravitational wave interferometer detectors and nanomechanical systems, we conclude that the deviations from quantum mechanics predicted by the continuous spontaneous localization (CSL) model of state vector reduction are at least five orders of magnitude below the relevant standard quantum limits for these experiments. The proposed LISA gravitational wave detector will be two orders of magnitude away from the capability of observing an effect.
I make some remarks on events leading to the final formulation of quantum chromodynamics, stimulated by the ``Search and Discovery''article by Bertram Schwarzschild in the December, 2004 {\it Physics Today}. The following text and references is being submitted as a letter to the editor of {\it Physics Today}.
We analyze the recently proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester, assuming that the mirror's dynamics contains a non-unitary term of the Lindblad type proportional to -[q,[q,ρ]], with q the position operator for the center of mass of the mirror, and ρthe statistical operator. We derive an exact formula for the fringe visibility for this system. We discuss the consequences of our result for tests of environmental decoherence and of collapse models. In particular, we find that with the conventional parameters for the CSL model of state vector collapse, maintenance of coherence is expected to within an accuracy of at least 1 part in 10^{8}. Increasing the apparatus coupling to environmental decoherence may lead to observable modifications of the fringe visibility, with time dependence given by our exact result.
I give an account of my involvement with the chiral anomaly, and with the nonrenormalization theorem for the chiral anomaly and the all orders calculation of the trace anomaly, as well as related work by others. I then briefly discuss implications of these results for more recent developments in anomalies in supersymmetric theories.
I describe how my involvement with monopoles related to the multimonopole existence proof of Taubes, and how my later work on quaternionic quantum mechanics led to the classification theorem for generalized projective group representations of Tao and Millard.
We continue the analysis of the possibility of supersymmetric $E_8$ as a family unification and grand unification theory, this time under the assumption that there is a vacuum gluino condensate, but that this condensate is {\it not} accompanied by dynamical generation of a mass gap in the pure $E_8$ gauge theory. Arguments supporting these assumptions are given. When the $E_8$ theory is coupled to supergravity, assuming vanishing of the cosmological constant and a supersymmetry breaking scale of around a TeV, we show that the gluino mass induced by gravitational coupling to the condensate is of order $10^{-3}$ eV or smaller, compatible with the fermion (and particularly the neutrino) mass spectrum. We suggest that composite scalar Higgs superfields can arise from a chiral glueball in the attractive 3875 channel (and possibly other channels), permitting the breaking of the original $E_8$ gauge group to a SO(10) grand unification group, times a SU(3) family symmetry group and an extra U(1) factor. A general analysis of the Higgs superpotential shows that in the absence of gravitational couplings, there is always a supersymmetric vacuum in the (unphysical) limit of infinite Higgs superfields. However, when gravitational couplings are included, dimensional analysis of the superpotential shows that the vacuum can be stabilized for finite Higgs superfields, with the occurrence of dynamical ${\cal F}$-type supersymmetry breaking. We conclude that an $E_8$ unification may be theoretically viable, providing an alternative paradigm for low energy model building, in which the supersymmetric partners of the standard model fermions are vectors, and in which the only chiral superfields are symmetry breaking Higgs fields.
We consider the partition function for a matrix model with a global unitary invariant energy function. We show that the averages over the partition function of global unitary invariant trace polynomials of the matrix variables are the same when calculated with any choice of a global unitary fixing, while averages of such polynomials without a trace define matrix-valued correlation functions, that depend on the choice of unitary fixing. The unitary fixing is formulated within the standard Faddeev-Popov framework, in which the squared Vandermonde determinant emerges as a factor of the complete Faddeev-Popov determinant. We give the ghost representation for the FP determinant, and the corresponding BRST invariance of the unitary-fixed partition function. The formalism is relevant for deriving Ward identities obeyed by matrix-valued correlation functions.
We generalize the Weisskopf-Wigner theory for the line shape and transition rates of decaying states to the case of the energy-driven stochastic Schrödinger equation that has been used as a phenomenology for state vector reduction. Within the standard approximations used in the Weisskopf-Wigner analysis, and assuming that the perturbing potential inducing the decay has vanishing matrix elements within the degenerate manifold containing the decaying state, the stochastic Schrödinger equation linearizes. Solving the linearized equations, we find no change from the standard analysis in the line shape or the transition rate per unit time. The only effect of the stochastic terms is to alter the early time transient behavior of the decay, in a way that eliminates the quantum Zeno effect. We apply our results to estimate experimental bounds on the parameter governing the stochastic effects.
We consider the classical dynamics of bosonic and fermionic matrix variables in complex Hilbert space, defined by a trace action, assuming cyclic invariance under the trace and the presence of a global unitary invariance. With plausible and explicitly stated assumptions, including the existence of a large hierarchy of scale between the underlying dynamics and observed physics, we show that (1) the equilibrium statistical mechanics of this matrix dynamics, in the canonical ensemble, gives rise to an emergent quantum mechanics for many degrees of freedom, including the standard canonical commutation/anticommutation relations and the usual unitary Heisenberg and Schrödinger picture time evolutions of operators and states, and (2) the fluctuation or Brownian motion corrections to this thermodyamics lead to an energy-driven stochastic modification of the Schrödinger equation, which is known to imply state vector reduction with Born rule probabilities. Thus, quantum mechanics and its probabilistic interpretation both arise as emergent phenomena in the underlying trace dynamics.
We discuss why, contrary to claims recently made by P. W. Anderson, decoherence has not solved the quantum measurement problem.
We review earlier proposals for $E_8$ family unification, and discuss why recent work of Kovner and Shifman on condensates in supersymmetric Yang-Mills theories suggests the reconsideration of $E_8$ supersymmetric Yang-Mills as a family unification theory.
We consider the energy-driven stochastic state vector reduction equation for the density matrix, which for pure state density matrices can be written in two equivalent forms. We use these forms to discuss the decoupling of the noise terms for independent subsystems, and to construct ``environmental'' stochastic density matrices whose time-independent expectations are the usual quantum statistical distributions. We then consider a measurement apparatus weakly coupled to an external environment, and show that in mean field (Hartree) approximation the stochastic equation separates into independent equations for the apparatus and environment, with the Hamiltonian for the apparatus augmented by the environmental expectation of the interaction Hamiltonian. We use the Hartree approximated equation to study a simple accretion model for the interaction of the apparatus with its environment, as part of a more general discussion of when the stochastic dynamics predicts state vector reduction, and when it predicts the maintenance of coherence. We also discuss the magnitude of decoherence effects acting during the reduction process. Our analysis supports the suggestion that a measurement takes place when the different outcomes are characterized by sufficiently distinct environmental interactions for the reduction process to be rapidly driven to completion.
We consider a generic supersymmetric matter theory coupled to linearized supergravity, and analyze scenarios for spontaneous symmetry breaking in terms of vacuum expectation values of components of the current supermultiplet. When the vacuum expectation of the energy momentum tensor is zero, but the scalar current or pseudoscalar current gets an expectation, evaluation of the gravitino self energy using the supersymmetry current algebra shows that there is an induced gravitino mass term. The structure of this term generalizes the supergravity action with cosmological constant to theories with CP violation. When the vacuum expectation of the energy momentum tensor is nonzero, supersymmetry is broken; requiring cancellation of the cosmological constant gives the corresponding generalized gravitino mass formula.
A number of authors have proposed stochastic versions of the Schrödinger equation, either as effective evolution equations for open quantum systems or as alternative theories with an intrinsic collapse mechanism. We discuss here two directions for generalization of these equations. First, we study a general class of norm preserving stochastic evolution equations, and show that even after making several specializations, there is an infinity of possible stochastic Schrödinger equations for which state vector collapse is provable. Second, we explore the problem of formulating a relativistic stochastic Schrödinger equation, using a manifestly covariant equation for a quantum field system based on the interaction picture of Tomonaga and Schwinger. The stochastic noise term in this equation can couple to any local scalar density that commutes with the interaction energy density, and leads to collapse onto spatially localized eigenstates. However, as found in a similar model by Pearle, the equation predicts an infinite rate of energy nonconservation proportional to $δ^3(\vec 0)$, arising from the local double commutator in the drift term.
This paper has been withdrawn, because the argument for generation of Goldstone modes is incorrect.