18,902 research outputs found

### A Strategy for a Vanishing Cosmological Constant in the Presence of Scale Invariance Breaking

Recent work has shown that complex quantum field theory emerges as a
statistical mechanical approximation to an underlying noncommutative operator
dynamics based on a total trace action. In this dynamics, scale invariance of
the trace action becomes the statement $0=Re Tr T_{\mu}^{\mu}$, with $T_{\mu
\nu}$ the operator stress energy tensor, and with $Tr$ the trace over the
underlying Hilbert space. We show that this condition implies the vanishing of
the cosmological constant and vacuum energy in the emergent quantum field
theory. However, since the scale invariance condition does not require the
operator $T_{\mu}^{\mu}$ to vanish, the spontaneous breakdown of scale
invariance is still permitted.Comment: Second award in the Gravity Research Foundation Essay Competition for
1997; to appear in General Relativity and Gravitation. Plain Tex, no figure

### Efficient Simulation of Quantum State Reduction

The energy-based stochastic extension of the Schrodinger equation is a rather
special nonlinear stochastic differential equation on Hilbert space, involving
a single free parameter, that has been shown to be very useful for modelling
the phenomenon of quantum state reduction. Here we construct a general closed
form solution to this equation, for any given initial condition, in terms of a
random variable representing the terminal value of the energy and an
independent Brownian motion. The solution is essentially algebraic in
character, involving no integration, and is thus suitable as a basis for
efficient simulation studies of state reduction in complex systems.Comment: 4 pages, No Figur

### Structure of Fluctuation Terms in the Trace Dynamics Ward Identity

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.Comment: TeX; 14 pages. Dedicated to Rafael Sorkin on the occasion of his 60th
birthda

### Response to the Comment by G. Emch on Projective Group Representations in Quaternionic Hilbert Space

We discuss the differing definitions of complex and quaternionic projective
group representations employed by us and by Emch. The definition of Emch
(termed here a strong projective representation) is too restrictive to
accommodate quaternionic Hilbert space embeddings of complex projective
representations. Our definition (termed here a weak projective representation)
encompasses such embeddings, and leads to a detailed theory of quaternionic, as
well as complex, projective group representations.Comment: 8 pages, Revtex, no figure

### No Eigenvalue in Finite Quantum Electrodynamics

We re-examine Quantum Electrodynamics (QED) with massless electron as a
finite quantum field theory as advocated by Gell-Mann-Low, Baker-Johnson,
Adler, Jackiw and others. We analyze the Dyson-Schwinger equation satisfied by
the massless electron in finite QED and conclude that the theory admits no
nontrivial eigenvalue for the fine structure constant.Comment: 13 pages, Late

### Schwinger Algebra for Quaternionic Quantum Mechanics

It is shown that the measurement algebra of Schwinger, a characterization of
the properties of Pauli measurements of the first and second kinds, forming the
foundation of his formulation of quantum mechanics over the complex field, has
a quaternionic generalization. In this quaternionic measurement algebra some of
the notions of quaternionic quantum mechanics are clarified. The conditions
imposed on the form of the corresponding quantum field theory are studied, and
the quantum fields are constructed. It is shown that the resulting quantum
fields coincide with the fermion or boson annihilation-creation operators
obtained by Razon and Horwitz in the limit in which the number of particles in
physical states $N \to \infty$.Comment: 20 pages, Plain Te

### Breaking quantum linearity: constraints from human perception and cosmological implications

Resolving the tension between quantum superpositions and the uniqueness of
the classical world is a major open problem. One possibility, which is
extensively explored both theoretically and experimentally, is that quantum
linearity breaks above a given scale. Theoretically, this possibility is
predicted by collapse models. They provide quantitative information on where
violations of the superposition principle become manifest. Here we show that
the lower bound on the collapse parameter lambda, coming from the analysis of
the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than the
original bound, in agreement with more recent analysis. This implies that the
collapse becomes effective with systems containing ~ 10^4 - 10^5 nucleons, and
thus falls within the range of testability with present-day technology. We also
compare the spectrum of the collapsing field with those of known cosmological
fields, showing that a typical cosmological random field can yield an efficient
wave function collapse.Comment: 13 pages, LaTeX, 3 figure

### Collapse models with non-white noises

We set up a general formalism for models of spontaneous wave function
collapse with dynamics represented by a stochastic differential equation driven
by general Gaussian noises, not necessarily white in time. In particular, we
show that the non-Schrodinger terms of the equation induce the collapse of the
wave function to one of the common eigenstates of the collapsing operators, and
that the collapse occurs with the correct quantum probabilities. We also
develop a perturbation expansion of the solution of the equation with respect
to the parameter which sets the strength of the collapse process; such an
approximation allows one to compute the leading order terms for the deviations
of the predictions of collapse models with respect to those of standard quantum
mechanics. This analysis shows that to leading order, the ``imaginary'' noise
trick can be used for non-white Gaussian noise.Comment: Latex, 20 pages;references added and minor revisions; published as J.
Phys. A: Math. Theor. {\bf 40} (2007) 15083-1509

### Ultrasonic measurement of porosity in casts and welds

The development of a quantitative nondestructive method which involves ultrasonic attenuation measurements in frequency domain to determine volume fraction of porosity in aluminum cast is discussed. The aluminum alloy A357 casting samples were produced at the Ohio State University Foundry with controlled porosity contents ranging from 0% to 6%. A computer controlled system was used to direct ultrasonic beam to a test sample to different places to conduct ultrasonic attenuation measurements. The plot of attenuation coefficients as a function of frequency was then evaluated based on existing theories to determine volume fraction of porosity and pore size

### Algebraic and geometric aspects of generalized quantum dynamics

\noindent We briefly discuss some algebraic and geometric aspects of the
generalized Poisson bracket and non--commutative phase space for generalized
quantum dynamics, which are analogous to properties of the classical Poisson
bracket and ordinary symplectic structure.Comment: 10pages,revtex, IASSNSHEP-93/5

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