scholarly journals Group Theory in Classical and Quantum Physics

Nature ◽  
1966 ◽  
Vol 211 (5047) ◽  
pp. 346-347
Author(s):  
B. L. MOISEIWITSCH
Keyword(s):  
Group Theory ◽  
Quantum Physics

scholarly journals The Topological Origin of Quantum Randomness

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 581
Author(s):  
Stefan Heusler ◽  
Paul Schlummer ◽  
Malte S. Ubben
Keyword(s):  
High School ◽  
Hilbert Space ◽  
Group Theory ◽  
Lorentz Group ◽  
Quantum Physics ◽  
Time Development ◽  
Mathematical Structures ◽  
Stochastic Nature ◽  
Quantum Randomness ◽  
And Topology

What is the origin of quantum randomness? Why does the deterministic, unitary time development in Hilbert space (the ‘4π-realm’) lead to a probabilistic behaviour of observables in space-time (the ‘2π-realm’)? We propose a simple topological model for quantum randomness. Following Kauffmann, we elaborate the mathematical structures that follow from a distinction(A,B) using group theory and topology. Crucially, the 2:1-mapping from SL(2,C) to the Lorentz group SO(3,1) turns out to be responsible for the stochastic nature of observables in quantum physics, as this 2:1-mapping breaks down during interactions. Entanglement leads to a change of topology, such that a distinction between A and B becomes impossible. In this sense, entanglement is the counterpart of a distinction (A,B). While the mathematical formalism involved in our argument based on virtual Dehn twists and torus splitting is non-trivial, the resulting haptic model is so simple that we think it might be suitable for undergraduate courses and maybe even for High school classes.

Representing Physical Phenomena

2018 ◽  
Author(s):  
Otávio Bueno ◽  
Steven French
Keyword(s):  
Quantum Mechanics ◽  
Group Theory ◽  
Liquid Helium ◽  
Quantum Physics ◽  
Scientific Work ◽  
Top Down ◽  
Partial Structures ◽  
Bose Einstein ◽  
Physical Phenomena

This chapter extends the case study on quantum mechanics to include not only the ‘top-down’ application of group theory to quantum physics but also the ‘bottom-up’ construction of models of the phenomena, with the example of London’s explanation of the superfluid behaviour of liquid helium in terms of Bose–Einstein statistics. We claim that in moving from top to bottom, from the mathematics to what is observed in the laboratory, the models involved and the relations between them can again be accommodated by the partial structures approach, coupled with an appreciation of the heuristic moves involved in scientific work. Furthermore, as in the previous examples, this case fits with our inferential account of the application of mathematics, whereby immersion of the phenomena into the relevant mathematics allows for the drawing down of structure and the derivation of certain results that can then be interpreted at the phenomenological level.

Applying New Mathematics

2018 ◽  
Author(s):  
Otávio Bueno ◽  
Steven French
Keyword(s):  
Quantum Mechanics ◽  
Group Theory ◽  
Quantum Physics ◽  
Practical Applications ◽  
Partial Structures ◽  
First Case ◽  
Suitable Framework

Here we present our first case study: the introduction of group theory into quantum mechanics in the 1920s and 1930s. It is helpful in this context to distinguish the ‘Weyl’ and ‘Wigner’ programmes, where the former is concerned with using group theory to provide secure foundations for the emerging quantum physics and the latter emphasizes its practical applications. We suggest the application of the mathematics to the physics depended on certain structural ‘bridges’ within the mathematics itself and also that both this mathematics and the physics were in a state of flux. Given those features, we argue that the partial structures approach offers a suitable framework for representing these developments. One can resist Steiner’s claim that the mathematics is doing all the work in these cases, as it is only because of prior idealizing moves on the physics side that the mathematics can be brought into play to begin with.

scholarly journals Towards the Unification of Quantum Dynamics, Relativity and Living Organisms

2018 ◽  
Author(s):  
Arturo Tozzi ◽  
James F. Peters ◽  
John S. Torday
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Group Theory ◽  
Quantum Dynamics ◽  
Quantum Physics ◽  
Binary Operation ◽  
Relativity Theory ◽  
Mathematical Framework ◽  
Mathematical Approach ◽  
Living Organisms

The unexploited unification of quantum physics, general relativity and biology is a keystone that paves the way towards a better understanding of the whole of Nature.  Here we propose a mathematical approach that introduces the problem in terms of group theory.  We build a cyclic groupoid (a nonempty set with a binary operation defined on it) that encompasses the three frameworks as subsets, representing two of their most dissimilar experimental results, i.e., 1) the commutativity detectable both in our macroscopic relativistic world and in biology; 2) and the noncommutativity detectable both in the microscopic quantum world and in biology.  This approach leads to a mathematical framework useful in the investigation of the three apparently irreconcilable realms.  Also, we show how cyclic groupoids encompassing quantum mechanics, relativity theory and biology might be equipped with dynamics that can be described by paths on the twisted cylinder of a Möbius strip.   

Quantum Physics

2004 ◽  
Author(s):  
Alastair I. M. Rae
Keyword(s):  
Quantum Physics

Quantum Physics

2006 ◽  
Author(s):  
Michel Le Bellac
Keyword(s):  
Quantum Physics
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