24,285 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 , with the operator stress energy tensor, and with 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 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
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
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
Poincar\'e Supersymmetry Representations Over Trace Class Noncommutative Graded Operator Algebras
We show that rigid supersymmetry theories in four dimensions can be extended
to give supersymmetric trace (or generalized quantum) dynamics theories, in
which the supersymmetry algebra is represented by the generalized Poisson
bracket of trace supercharges, constructed from fields that form a trace class
noncommutative graded operator algebra. In particular, supersymmetry theories
can be turned into supersymmetric matrix models this way. We demonstrate our
results by detailed component field calculations for the Wess-Zumino and the
supersymmetric Yang-Mills models (the latter with axial gauge fixing), and then
show that they are also implied by a simple and general superspace argument.Comment: plaintex, 23 Page
Anomalies to All Orders
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.Comment: 35 pages, latex; To appear in Fifty Years of Yang-Mills Theory, G. 't
Hooft editor, to be published by World Scientific. Final version; references
adde
symmetry breaking by rank three and rank two antisymmetric tensor scalars
We study symmetry breaking by rank three and rank two antisymmetric
tensor fields. Using tensor analysis, we derive branching rules for the adjoint
and antisymmetric tensor representations, and explain why for general
one finds the same generator mismatch that we noted earlier in special
cases. We then compute the masses of the various scalar fields in the branching
expansion, in terms of parameters of the general renormalizable potential for
the antisymmetric tensor fields.Comment: Latex, 11 pages; v2 has a minor revision above Eq. (30
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