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There is no essential contradiction between the definitions in the two references that you gave, except that the one given in the nLab entry is more general. Sternberg defines the Lagrangian (functio …

Since the question asked for a reference for this relation between the Fourier and Legendre transforms, here's one: Guillemin & Sternberg, Geometric Asymptotics (AMS, 1990). See in particular the …

G. Scharf, Quantum Gauge Theories: Spin One and Two http://books.google.com/books?id=DsFauPtuAoYC (can be downloaded as a PDF) https://books.google.de/books?id=0DvBDAAAQBAJ (it seems the book c …

The following is an elaboration of the point of view that spinors are "square roots" of vectors (or rather of isotropic vectors). I will restrict my attention to 3-dimensional Euclidean vectors, becau …

If I read your updated question correctly, you are asking whether people have considered non-linear modifications of quantum mechanics in order to accommodate interacting QFTs. I'm sure someone, somew …

Both proofs in the question are of the following type. Suppose you want to prove a certain identity among numbers $X$, say $f(X)=0$. If you can find another function $g(X,Y)$ such that $f(X)=g(X,Y)$ f …

I believe these integrals can be evaluated directly in the $\varepsilon=0$ limit by interpreting the result of the inner integral as a distribution. $$ \int\limits_0^\infty dq \, q^{n+1} \, e^{iq(\tau …

I will add here some more details to expand my comment. Any two functions $Y_1(x^3,x^4)$ and $Y_2(x^3,x^4)$ give local coordinates on any open domain of the $(x^3,x^4)$-plane where their Jacobian dete …

Your argument starts with the assumption that there is such a thing as a "Euclidean free scalar field", as an operator valued function or distribution. And this is where it goes wrong. Obviously, you …

Here's a trick to recover the fermionic signs, knowing the bosonic formulas. First, introduce a sufficient number of algebraically independent "c-numbers" $\epsilon_k$, that are only required to anti- …

For Lorentzian geometry (which uses the same formulas as Riemannian geometry up to a few signs) you can find a pretty concise definition of this determinant and the equivalence of these two formulas i …

Connection of functional derivative with variational derivative: $\frac{\delta}{\delta\phi(x)} F[\phi] = \frac{\delta F[\phi]}{\delta\phi}(x)$. Note that the variational derivative carries an extra co …

If you are happy with the interpretation you give at the bottom of your question for the correlation function $G_2(x,y)=\langle0|\phi(x)\phi(y)|0\rangle$ for a quantum field on Minkowski space, then i …

Some physical background is needed to interpret phrases like these. In quantum mechanics, interactions between two particles (either composite or elementary) are described by an operator, called a Ham …

To clarify, for those who have not looked at the reference, the integral identity in question is $$ \int_{\mathbb{R}^d} \frac{d^dq}{(q^2)^{\nu_1} ((k-q)^2)^{\nu_2}} = \frac{\Gamma(d/2-\nu_1)\Gamma …