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I'm trying to learn some quantum mechanics by myself, and because of my mathematics background, I'm trying to understand it in a rigorous way. Since then, I've been intrigued by the use of rigged Hilb …

I'm looking for good references to learn about the mathematical foundations of quantum mechanics. By mathematical foundations, I do not mean rigorous quantum mechanics in general but the axioms behind …

Let us define a pure vector state of a quantum system as a vector $\psi$ in a Hilbert space $\mathscr{H}$ with norm $\|\psi\| = 1$. Let $\mathscr{B}(\mathscr{H})$ be the Banach space of bounded linear …

When I started studying the basics of $\phi^{4}_{d}$, I looked for papers or lecture notes which would give me some general ideas about the topic and which would construct and/or prove the basic resul …

Wedge products and exterior powers are discussed in W. Greub's book Multilinear algebra as follows. Definition: Let $E$ be an arbitrary vector space and $p \ge 2$. Then a vector space $\bigwedge^{p}E$ …

I have been taking a look at some papers in constructive quantum field theory and I got the impression that there is a systematic of estimating things like e.g the effective action or the free energy …

I was reading Constructive Renormalization Group by V. Rivasseau and I got some points which I would like to clarify. On page 2, Rivasseau talks about the large field problem and, if I understood it c …

To this day, it is known that a satisfying mathematical formulation of quantum field theory is far from sight, even though some noninteracting theories can be described in rigorous mathematical langua …

This is actually a more elaborated version of a previous question of mine, which is now deleted. First, some quick notations: (1) $\Omega_{0} := \{-1,1\}$ and $\mathcal{F}_{0} := 2^{\Omega_{0}}$ are, …

Let $\mathscr{H}$ be a complex Hilbert space and $A$ be an Hermitian operator $A: \mathscr{H}\to \mathscr{H}$. Suppose, for a moment, that $A$ has a set of discrete eigenvalues $\{\lambda_{n}\}_{n\in …

Let $\mathcal{H}$ be a finite-dimensional inner product space over $\mathbb{C}$. Suppose $A_{1},...,A_{N}$ are linear operators on $\mathcal{H}$ such that: $$\{A_{i},A_{j}\} = 0 \quad \mbox{and} \quad …

I've discovered Adam's lecture notes on statistical mechanics after posting my first question about Minlo's discussion on continuous Gibbs measures. Adam's lecture notes are really good, but there is …

This is a second part of my previous question, which I decided to split into two parts not to mix up different topics at one giant question. Again, according to V. Rivasseau (section 1.5 of Constructi …

I am studying the following Schrödinger equation: $$(-\Delta + w)f = 0$$ which represents a quantum state with zero energy. Here $w$ and $f$ are defined on $\mathbb{R}^{3}$. For simplicity, let us ass …

Are there good references for (both zero and finite time) interacting systems of quantum many-body theory? More precisely, I would be interested in references discussing the following topics: Second …