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#### 1Grassmann Algebra Book

Some of the things you can do with the GrassmannAlgebra software. You can: * Set up your own space of any dimension and metric. The default is a 3D Euclidean * Work basis-free or with a basis * Declare your own scalar symbols * Declare your own vector symbols: * Apply Grassmann operations. A Grassmann operation is any of: the complement operation and the six product operations: the exterior, regressive, interior, generalized Grassmann, hypercomplex and Clifford products. * Manipulate Grassmann expressions and numbers. A Grassmann expression is either a scalar, a Grassmann variable, or the result of a sequence of Grassmann operations or sums on Grassmann expressions. A Grassmann number is a Grassmann expression expressed as a linear combination of basis elements. * Compute the grade of any Grassmann expression. * Query the attributes of any expression. * Extract components of different types
6 years ago by @draganigajic
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#### 1Determinism, locality, and meta-time

This essay is about two properties that some theories of physics have — determinism and locality — and the gaps that can exist between how they are understood as properties of physical reality, how they are understood as properties of mathematical theories, and how they are formally defined as properties of mathematical theories. I will point out one such gap that seems to have gone widely unremarked, and that could admit an interesting class of physical theories. On the other hand, for readers already well acquainted with Bell's Theorem, it may be helpful to know up front that, ultimately, I will identify a particular class of mathematical theories that have a sort of locality —mathematical locality, but not apparently physical locality— but that do not satisfy the assumptions of the Theorem and therefore are not constrained by Bell's Inequality (and no, this is not related to Joy Christian's work; I'm going to take an orthodox view of Bell's Theorem).
6 years ago by @draganigajic
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#### 2Transactional Interpretation of Quantum Mechanics, The

Review of Modern Physics 1986 The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen Interpretation (CI) of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the Transactional Interpretation (TI), is presented. The basic element of TI is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The TI is explicitly nonlocal and thereby consistent with recent tests of the Bell Inequality, yet is relativistically invariant and fully causal. A detailed comparison of the TI and CI is made in the context of well known quantum mechanical gedanken experiments and "paradoxes". The TI permits quantum mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the CI.
6 years ago by @draganigajic
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#### 1[math-ph/0602036] Algebraic Quantum Field Theory

Abstract: Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also . 202 pages; to appear in Handbook of the Philosophy of Physics
6 years ago by @draganigajic
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