All Questions
23
questions
3
votes
2
answers
148
views
Algebraic QFT from a Lagrangian
In physics, the fundamental description of physical theories frequently revolves around the concept of a Lagrangian. My expertise encompasses diverse algebraic formulations within the domain of ...
- 368
2
votes
1
answer
116
views
What's the exact definition of fields in conformal field theory?
For example we work with a 2d scalar field $\phi$. I guess $\phi$, $\partial_z\phi$, $\partial_{\bar z}\phi$ are fields, are there more? Is it true that all fields are in the form of $\partial_z^i\...
- 249
9
votes
4
answers
3k
views
If quantum fields are operator valued distributions, why aren't they always smeared?
I don't completely understand the distributional character of a quantum field because I never see them "smeared" in basic textbooks. As I understand it, if $\chi : \mathcal{F} \rightarrow \...
- 615
3
votes
1
answer
153
views
Equivalence of Schrödinger operator formalism and Path Integral Formulations for Scalar Field Theory
I'm exploring the deep connections between different formulations of quantum field theories and have a specific question about the equivalence between the Schrödinger representation and the path ...
- 1,548
2
votes
1
answer
119
views
Understanding mathematically the promotion of field/observable to operator in QFT
First, I know it "worked", in physics sense.
My question is what happened in the math sense.
When promoting something, such as a field, to an operator, am I essentially mapping the field to ...
- 63
12
votes
2
answers
2k
views
How to interpret quantum fields?
As an analogy of what I am looking for, suppose $f(x,t)$ represents a classical field. Then we may interpret this as saying at position $x$ and time $t$ the field takes on a value $f(x,t)$.
In quantum ...
- 3,350
2
votes
1
answer
410
views
Wave functions, Ket vectors and Dirac equation: why can't I use ket formulation on Dirac equation?
From non-relativistic quantum mechanics, a $\frac{1}{2}$- spin system can be represented by a ket vector like:
$$|\psi\rangle = a|+\rangle_{z}+b|-\rangle_{z}. \tag{1}$$
The object on $(1)$, is a ket ...
- 315
10
votes
1
answer
830
views
Why do we need a boundary condition in quantum field theories?
When we discuss quantum field theory defined on manifolds with a boundary, we always choose a boundary condition for the fields. And the argument usually says that we need the boundary condition to ...
- 129
5
votes
2
answers
734
views
Why are only positive frequency mode functions allowed in Quantum field theory? How is this consistent with anti particles having negative energy?
In quantum field theory, one can redefine the particle creation and annihilation operators using Bogoliobov transformations, which can give rise to a different vacuum state, using a new set of ...
- 427
1
vote
0
answers
265
views
Finite norm for solutions of K.G. equation
Before getting into my actual question, let me give an example of a similar problem and its solutions. In non-relativistic wave function quantum mechanics, one usually assigns the Hilbert space of the ...
- 1,056
1
vote
2
answers
583
views
Vacuum fluctuations of quantum scalar field
Consider a free scalar quantum field
$$ H = \int d^3 x \left( \, \Pi(x)^2+(\nabla\phi(x))^2 \right). $$
Introducing the creation and annihilation operators we find the "vacuum catastrophe"
$$...
- 1,037
7
votes
1
answer
635
views
What are some good references for field theory via functional analysis?
Many of the aspects of QFT are traditionally done in ways incompatible with a rigorous mathematical treatment, calling for a variety of tricks to fix essentially what was caused by unjustified ...
3
votes
2
answers
881
views
Explicit form of the wavefunctional
In quantum mechanics, one in principle can write down an explicit form of the corresponding wave-function. For example, $V_i$ for the $i$-th level of quantum harmonic oscillator.
In QFT, the Hilbert ...
0
votes
0
answers
66
views
Second quantisation for dynamical systems
The paper "Perturbative approach to an $A + B \rightarrow C$ reaction-diffusion system", (Z. Phys. B 96, 137-144 (1994)), by Conrad and Trimper, applies the Fock Space formalism for the ...
- 141
3
votes
1
answer
265
views
What is the overlap $\langle \phi | 0 \rangle$ for a scalar field?
Consider a massive free real scalar field $\hat{\Phi}$ (with $\mathcal{L}[\Phi] = \partial_{\mu}\Phi\partial^\mu \Phi
- \tfrac{1}{2} m^2 \Phi^2$). I was wondering what is the overlap for the ...
- 3,719