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edited Apr 9, 2013 at 4:29

Anatoly Kochubei

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The above answers and comments do not mention monographs giving detailed expositions of non-Archimedean quantum mechanics and related subjects in analysis. See

V.S. Vladimirov, I.V. Volovich, and E.I. Zelenov, p-Adic Analysis and Mathematical Physics, World Scientific, 1994,

for quantum mechanics on $\mathbb Q_p$ with complex-valued wave functions, and

A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer, 1997,

for a completely non-Archimedean theory. Analysis over fields of positive characteristic including such things as representations of canonical commutation relations of quantum mechanics is given in

A.N. Kochubei, Analysis in Positive Characteristic, Cambridge University Press, 2009.

For the spectral theorem in the non-Archimedean case see A.N. Kochubei, Non-Archimedean normal operators, J. Math. Phys. 51 (2010), article 023526.

All the above are in fact not toy models, but the exploration of mathematical subjects emerging as one tries to develop non-Archimedean quantum theory. They are undoubtely interesting though it remains to be seen whether they correspond to any realistic physics.

The above answers and comments do not mention monographs giving detailed expositions of non-Archimedean quantum mechanics and related subjects in analysis. See

V.S. Vladimirov, I.V. Volovich, and E.I. Zelenov, p-Adic Analysis and Mathematical Physics, World Scientific, 1994,

for quantum mechanics on $\mathbb Q_p$ with complex-valued wave functions, and

A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer, 1997,

for a completely non-Archimedean theory. Analysis over fields of positive characteristic including such things as representations of canonical commutation relations of quantum mechanics is given in

A.N. Kochubei, Analysis in Positive Characteristic, Cambridge University Press, 2009.

For the spectral theorem in the non-Archimedean case see A.N. Kochubei, Non-Archimedean normal operators, J. Math. Phys. 51 (2010), article 023526.

All the above are in fact not toy models, but the exploration of mathematical subjects emerging as one tries to develop non-Archimedean quantum theory. They are undoubtely interesting though it remains to be seen whether they correspond to any realistic physics.

The above answers and comments do not mention monographs giving detailed expositions of non-Archimedean quantum mechanics and related subjects in analysis. See

V.S. Vladimirov, I.V. Volovich, and E.I. Zelenov, p-Adic Analysis and Mathematical Physics, World Scientific, 1994,

for quantum mechanics on $\mathbb Q_p$ with complex-valued wave functions, and

A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer, 1997,

for a completely non-Archimedean theory. Analysis over fields of positive characteristic including such things as representations of canonical commutation relations of quantum mechanics is given in

A.N. Kochubei, Analysis in Positive Characteristic, Cambridge University Press, 2009.

All the above are in fact not toy models, but the exploration of mathematical subjects emerging as one tries to develop non-Archimedean quantum theory. They are undoubtely interesting though it remains to be seen whether they correspond to any realistic physics.

Source Link

created Mar 21, 2011 at 5:59

Anatoly Kochubei

4.9k
1
27
23

The above answers and comments do not mention monographs giving detailed expositions of non-Archimedean quantum mechanics and related subjects in analysis. See

V.S. Vladimirov, I.V. Volovich, and E.I. Zelenov, p-Adic Analysis and Mathematical Physics, World Scientific, 1994,

for quantum mechanics on $\mathbb Q_p$ with complex-valued wave functions, and

A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer, 1997,

for a completely non-Archimedean theory. Analysis over fields of positive characteristic including such things as representations of canonical commutation relations of quantum mechanics is given in

A.N. Kochubei, Analysis in Positive Characteristic, Cambridge University Press, 2009.

For the spectral theorem in the non-Archimedean case see A.N. Kochubei, Non-Archimedean normal operators, J. Math. Phys. 51 (2010), article 023526.

All the above are in fact not toy models, but the exploration of mathematical subjects emerging as one tries to develop non-Archimedean quantum theory. They are undoubtely interesting though it remains to be seen whether they correspond to any realistic physics.