Search results for " Quantum mechanics"
showing 10 items of 245 documents
The Dynamical Problem for a Non Self-adjoint Hamiltonian
2012
After a compact overview of the standard mathematical presentations of the formalism of quantum mechanics using the language of C*- algebras and/or the language of Hilbert spaces we turn attention to the possible use of the language of Krein spaces.I n the context of the so-called three-Hilbert-space scenario involving the so-called PT-symmetric or quasi- Hermitian quantum models a few recent results are reviewed from this point of view, with particular focus on the quantum dynamics in the Schrodinger and Heisenberg representations.
Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent whole
The theoretical framework behind TGD involves several different strands and the goal is to unify them to a single coherent whole. TGD involves number theoretic and geometric visions about physics and $M^8-H$ duality, analogous to Langlands duality, is proposed to unify them. Also quantum classical correspondence (QCC) is a central aspect of TGD. One should understand both the $M^8-H$ duality and QCC at the level of detail. The following mathematical notions are expected to be of relevance for this goal. \begin{enumerate} \item Von Neumann algebras, call them $M$, in particular hyperfinite factors of type $II_1$ (HFFs), are in a central role. Both the geometric and number theoretic side, QCC…
Some New Ideas Related to Langlands Program viz. TGD
Langlands' program seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. Langlands program is described by Edward Frenkel as a kind of grand unified theory of mathematics. In the TGD framework, $M^8-M^4\times CP_2$ duality assigns to a rational polynomial a set of mass shells $H^3$ in $M^4\subset M^8$ and by associativity condition a 4-D surface in $M^8$, and its it to $H=M^4\times CP_2$. $M^8-M^4\times CP_2$ means that number theoretic vision and geometric vision of physics are dual or at least complementary. This vision could extend to a trinity of number theoretic, geometric and topologica…
Bohm’s Implicate Order, Wheeler’s Participatory Universe, Stapp’s Mindful Universe, Zurek’s Quantum Darwinism and the Buddhist Mind-Only Ground Consc…
According to quantum physicist Erich Joos the following three issues are the outstanding quantum conundrums of deep significance: 1. The meaning of the wavefunction; 2. The exact nature of the mechanism of the collapse; 3. The connection between the quantum and classical realm. In this paper I shall attempt to elucidate a possible approach to these central issues by drawing parallels between David Bohm’s notion of the implicate order, John Wheeler’s vision of the ‘Participatory Universe’, Henry Stapp’s account of the Heisenberg-von Neumann quantum ‘ontology’, Wojciech Zurek’s ‘Quantum Darwinism’ proposal and the Buddhist Mind-Only (Yogachara–Chittamatra) concept of the alayavijnana, the gro…
About the role of Galois groups in TGD framework
2021
This article was inspired by the inverse problem of Galois theory. Galois groups are realized as number theoretic symmetry groups realized physically in TGD a symmetries of space-time surfaces. Galois confinement is as analog of color confinement is proposed in TGD inspired quantum biology. Two instances of the inverse Galois problem, which are especially interesting in TGD, are following: Q1: Can a given finite group appear as Galois group over Q? The answer is not known. Q2: Can a given finite group G appear as a Galois group over some EQ? Answer to Q2 is positive as will be found and the extensions for a given G can be explicitly constructed.
Generalization of thermodynamics allowing negentropic entanglement and a model for conscious information processing
2011
Costa de Beauregard considers a model for information processing by a computer based on an analogy with Carnot's heat engine. I am grateful for Stephen Paul King for bringing this article to my attention in Time discussion group and also for inspiring discussions which also led to the birth of this section. As such the model Beauregard for computer does not look convincing as a model for what happens in biological information processing. Combined with TGD based vision about living matter, the model however inspires a model for how conscious information is generated and how the second law of thermodynamics must be modified in TGD framework. The basic formulas of thermodynamics remain as such…
The problems of the dialogue of quantum mechanics and theology
2005
The paper is a review of bordering problems between quantum mechanics, describing the microworld, and Christian theology. The basic concepts of quantum mechanics and their essential distinctions from our notions about the macroworld are given in a popular way. The outlined methodological principles of quantum mechanics are used as an analogy for the illustration of Christian faith miracle, taking as an example the celebration of Holy Communion. The problem of relationships between the methodology of quantum mechanics and the observer’s consciousness is analyzed. The critical appraisal of the many-worlds interpretation of quantum mechanics is given. The possibilty of a deeper understanding o…
Analytic structure ofϕ4theory using light-by-light sum rules
2013
Abstract We apply a sum rule for the forward light-by-light scattering process within the context of the ϕ 4 quantum field theory. As a consequence of the sum rule a stringent causality criterion is presented and the resulting constraints are studied within a particular resummation of graphs. Such resummation is demonstrated to be consistent with the sum rule to all orders of perturbation theory. We furthermore show the appearance of particular non-perturbative solutions within such approximation to be a necessary requirement of the sum rule. For a range of values of the coupling constant, these solutions manifest themselves as a physical bound state and a K-matrix pole. For another domain …
Causality and the Coulomb sum rule in nuclei.
1989
The spectral function in the Jost-Lehmann-Dyson representation of causal commutators is determined for the nonrelativistic limit of inclusive lepton scattering from nuclei. From this an extrapolation of the Coulomb sum rule to higher-momentum transfers is performed which is consistent with the requirement of causality.
Process-independent strong running coupling
2016
We unify two widely different approaches to understanding the infrared behaviour of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realised via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running-coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann--Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be…