# Tag Info

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The Brownian motion $x(t)$ is non-differentiable, so a particular trajectory $x(t)$ can't extremize an action $S$ which would be a functional of $x(t)$ and its derivative, $\dot x(t)$, because the derivative isn't even well-defined and any expression of the type $\int [\dot x(t)]^2 dt$, the usual kinetic term in the action, diverges. (See e.g. middle of page ...

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Brian Hall "Quantum Theory for Mathematicians" is a recent nice book that presents the basics of QM with mathematical rigor, as suggested by the title. It covers a fair amount of topics, and seems suitable for an undergraduate level. The short book of Mackey "Mathematical foundations of Quantum Mechanics" is also a very nice book on the axiomatization of QM, ...

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I recommend two resources: Feynman's original book called Quantum Mechanics and Path Integrals. This contains most of the prerequisites in the first two chapters, but you will need some maturity to get through them. A. Zee's quantum field theory book Quantum Field Theory in a Nutshell for its friendly chapter on them.

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To study the precise mathematical formulation of path integrals, you actually need probabilistic tools. The path integral is a stochastic integral with suitable measures, such as the Wiener measure associated with brownian motion. The ideas used by physicists are very useful, but not always mathematically accurate, and rely more or less on justification by ...

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I believe it was Boltzmann who first made the connection between entropy and micro states. chapter 12 of "Classical and Statistical Thermodynamics" by Ashley H. Carter discusses Boltzmann's arguments. To summarize from that book: Entropy ($S$) corresponds to a particular configuration of an ensemble of particles called a macro state. A macro state can be ...

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Quantum Mechanics and Path Integrals: This is a book every physicist, or student of physics, should study. Here the author describes the principle of action in quantum physics. It is not a minimum action principle, like in classical mechanics: you can, however, derive the classical minimum principle from it, in the classical limit. Why is this important? ...

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Feynman's path integral formulation is closely related to the action principle of classical mechanics, which relies heavily on the calculus of variations. You need to learn, essentially, how to minimize a functional. Prerequisites are pretty much just calculus (multivariable, hopefully), as well some classical mechanics to understand the motivation behind ...

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John R. Taylor's Classical Mechanics has a couple of chapters on Lagrange and Hamilton that I found very helpful.

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I think Adam's answer is excellent, and I'd rather make this a comment but can't as I just signed up in order to answer. While I agree with most of what Adam said, there are cases where large-N works well for $N=1$. The case I'm familiar with is the large-N expansion for the "Spin Ices" Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$, which have Ising spins on a ...

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I am a great fan of Albert Messiah, 'Quantum Mechanics', now available (two volumes bound as one) in a sturdy paperback from Dover, at reasonable cost. Don't know why this has dropped out of fashion-- people complain it is too much oriented towards nuclear physics. Well I am a physical biochemist turned magnetic resonance jock, and I find it excellently ...

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Try exploring the National Nuclear Data Center. If I search the Evaluated Nuclear Structure Data File for "incident particle: g" and "outgoing particle: g" I get datasets for most, but not all, nuclei. There are other databases hosted by the NNDC as well, and all are well-referenced to the experimental literature.

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This is a hard question to answer, in the end. However, be assured that long, long, ago we started looking for nuclear expositions by looking for X and gamma radiation using the Vela satellites http://en.wikipedia.org/wiki/Vela_(satellite) . These did not find much in the way of violations of the nuclear test ban treaties but did discover astronomical ...

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The two books on my shelf that I regularly thumb through are: Galactic Dynamics by Binney and Tremaine Galaxy Formation and Evolution by Mo, van den Bosch and White You can probably tell from the titles that neither is a general astronomy text. I find both to be excellent graduate-level texts on their topics. Galactic Dynamics is a classic from the '70s, ...

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Schrödinger's work is known for two distinct ideas relating to the nature of living systems. The first is what he called "order from disorder," meaning the way in which organisms can maintain a low entropy (or high free energy) state by increasing the entropy of their environment. (I.e. by eating low-entropy food and excreting high-entropy waste). Although ...

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Perhaps you are starting by the wrong end. Your concern seems to be related in the first term with the totally misleading notation of integrals in quantum mechanics, and this is more related with the spectral theorem than with distributions itself. Distributions only appear in Quantum mechanics when certain operators has empty spectrum in the usual Hilber ...

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This is a very difficult problem. I try to explain why. If we want to obtain the mathematical proof of the second law, we must consider the mathematical proof of the entropy first, as a state function. Clausius’ definition $dS=δQ/T$ cannot be proven in mathematics, as an exact differential, so the definition $dS=δQ/T$ must depend on imaginary reversible ...

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