5
votes
3answers
329 views

Why is normal ordering a valid operation?

Why is normal ordering even a valid operation in the first place? I mean it can give us some nice results, but why can we do the ordering for the operators like that? Is its definition motivated by ...
5
votes
1answer
133 views

How do instantons cause vacuum decay?

From what I read about on instantons (Zee, QFT in a Nutshell, pg 309-310), an instanton is a vacuum solution that maps $S^3 \rightarrow S^3$ (the boundary of Euclideanized spacetime), which comes from ...
4
votes
1answer
104 views

The relation between classical and quantum vacua

First let me clarify what I mean by vacuum. Suppose we are concerned with a theory of fields $\phi ^i$ defined on a stationary globally hyperbolic spacetime $M$ (I want the spacetime to be stationary ...
4
votes
1answer
84 views

Tadpole diagram and vacuum

This statement may be well-known. For many massless theories, these tadpole diagram graphs vanish in dimensional regularization (by dimensional analysis and the absence of any inherent mass scale in ...
5
votes
0answers
99 views

Could energy be stored into (not extracted from) the quantum zero point field (like a battery)?

In order to explain the question clearly, I will make a short introduction. In 1962, Josephson predicted that for a sufficiently thin insulating layer, it should be possible for Cooper pairs to ...
2
votes
3answers
330 views

why cannot fermions have non-zero vacuum expectation value?

In quantum field theory, scalar can take non-zero vacuum expectation value(vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory ...
1
vote
1answer
169 views

What is the meaning of the negative vacuum expectation value of the Higgs field? Do we see it in nature?

In studying about the Higgs field and related, I find little mention of the equilibrium point at -V. I would like help conceptualizing what a negative vacuum expectation value is, ideally with respect ...
4
votes
1answer
133 views

Does $\langle\Omega|\mathrm{e}^{\mathrm{i}Px}=\langle\Omega|\mathrm{e}^{\mathrm{i}0x}$? $(\langle\Omega| =$ ground state of the interacting theory)

Let $\langle\Omega|$ be the ground state of an interacting theory, just as Peskin & Schroeder(PS) describes on page 82 and page 213. On page 213 PS do the following ...
4
votes
1answer
112 views

Definition of vacuum in field theory; Connection between the classical definition and the connection to QFT

I am a bit confused by what is defined to be a vacuum in field theory. Classically a vaccum state is defined to be the state where the field sits at some minima of the potential $\frac{\partial ...
1
vote
1answer
138 views

Expectation values in QFT?

What is the meaning of different expectation values in QFT? For instance: $$\langle 0|{\cal O}(0)|q,s\rangle$$ or $$\langle 0|{\cal O}(0)|0\rangle$$ with ${\cal O}$ being some operator and ...
1
vote
1answer
213 views

Vacuum expectation value in QFT

In QFT, one writes the VEV of a field $\psi$ as $\langle0|\psi|0\rangle$. But as I understand it, the fields in QFT are not operators, but just some functions which we use to calculate cross-sections. ...
1
vote
1answer
90 views

are there any “known unknowns” that could affect the possibility of a false vacuum?

(Although Donald Rumsfeld was mocked for talking about "known unknowns" and "unknown unknowns", I think it's an truly important distinction.) Periodically, I hear about how the universe might be in a ...
4
votes
2answers
161 views

Why Goldstone Bosons? (A Question about VEVs)

I understand how the mechanism of spontaneous symmetry breaking works, and why it produces Goldstone bosons (for global symmetries) and massive gauge bosons (for local ones). However, I'm confused as ...
5
votes
0answers
131 views

What does $\text{VAC}$ mean in Weinberg's QFT?

Hopefully Weinberg is sufficiently popular that this question isn't too localized. I'm reading Volume II (16.1, p. 63) and he refers to the state $\lvert\text{VAC}\rangle$ quite a lot. Does this mean ...
2
votes
1answer
206 views

Symmetry Breaking and Vacuum Expectation Values

Consider a real scalar field $\phi$ in a theory with a Lagrangian $$ \mathcal{L}:=-\frac{1}{2}\partial _\mu \phi \partial ^\mu \phi -V(\phi ), $$ where $$ V(\phi ):= -\mu ^2\phi ...
2
votes
2answers
296 views

Vacuum Expectation Value and the Minima of the Potential

Often times in quantum field theory, you will hear people using the term "vacuum expectation value" when referring to the minimum of the potential $V(\phi )$ in the Lagrangian (I'm pretty sure every ...
9
votes
1answer
488 views

The vacuum in quantum field theories: what is it?

In Section 10.1 of his textbook Quantum Field Theory for Mathematicians, Ticciati writes Assuming that the background field or classical source $j(x)$ is zero at space-time infinity, the presence ...
2
votes
5answers
1k views

Nothing vs. empty space

This question quotes Hawking saying: [...] you enter a world where conjuring something out of nothing is possible (at least, for a short while). That's because at this scale particles, such as ...
1
vote
2answers
1k views

Are quantum fluctuations completely uncaused events?

I read here that particles/antiparticles appear and annihilate each other spontaneously in empty space. Since particles appear and disappear in empty space, it would seem that empty space has some ...
4
votes
1answer
202 views

de Sitter versus Minkowski QFT and cosmological constant

WMAP/Planck results confirm than we live in a de Sitter-like phase, i.e., a Universe with positive acceleration or positive cosmological constant! Therefore, I believe that a way to solve the ...
2
votes
0answers
234 views

Vacuum to vacuum transition amplitude

I have two questions about Vacuum to vacuum transition amplitude. Can any particle stay in $|0\rangle$? I was studying this topic from Srednicki's QFT book. He writes in eq.$(6.22)$ $$\langle0|0 ...
1
vote
1answer
196 views

Multiple vacua vs. vev's in qft

Take a (possibly supersymmetric) relativistic quantum field theory: when we construct it, we suppose that there is a unique vacuum state $|0\rangle$ which is Lorentz invariant, vector of some Hilbert ...
1
vote
2answers
479 views

What is the expectation value of the number operator when the vacuum has a VEV?

The number operator N applied to a field whose vacuum has zero VEV gives $N|0>=0$. What if we apply it to the Higgs field? The background of this question is that in popular scientific accounts, ...
4
votes
3answers
647 views

Creation of particle anti-particle pairs

I was reading some QFT notes and there is one point that I don't understand, they are justifying why we need QFT saying that the number of particles is not preserved once we consider special ...
7
votes
3answers
673 views

What really goes on in a vacuum?

I've been told that a vacuum isn't actually empty space, rather that it consists of antiparticle pairs spontaneously materialising then quickly annihilating, which leads me to a few questions. ...
2
votes
2answers
549 views

Why $\lambda\phi^4$ theory, where $\lambda>0$, is not bounded from below?

Why the following interaction, in QFT, $$\displaystyle{\cal L}_{\rm int} ~=~\frac{\lambda}{4!}\phi^4$$ where $\lambda$ is positive, represents a theory that is unstable (or unbounded from below as it ...
15
votes
4answers
1k views

Is there an intuitive description of vacuum entanglement?

People often refer to the fact that the vacuum is an entangled state (It's even described as a maximally entangled state). I was trying to get a feeling for what that really means. The problem is ...
8
votes
1answer
1k views

Measured Higgs mass and vacuum stability

There is such a thing, called "stability bound" on mass of the Higgs boson. The basic idea (as I understand it) is that we take Higgs self-coupling, and calculate its renormalization running. And it ...
2
votes
2answers
100 views

Is there any correlation between the energy density fluctuations of two separate systems in a vacuum state?

I think the title says it all. What I am curious to find out is if there are any observable changes in the fluctuations of zero-point energy in a vacuum state system that are the consequence of ...
4
votes
1answer
402 views

Does the vacuum energy problem of quantum field theory only occur in the Hamiltonian approach, or also in the path integral approach and in AQFT?

In a standard QFT class, you're being indoctrinated that there is the "infinite vacuum energy density problem". (This is sometimes paraphrased as the "cosmological constant problem", which is in my ...
9
votes
3answers
2k views

What are the calculations for Vacuum Energy?

In wiki the Vacuum Energy in a cubic meter of free space ranges from $10^{-9}$ from the cosmological constant to $10^{113}$ due to calculations in Quantum Electrodynamics (QED) and Stochastic ...
4
votes
0answers
257 views

Stability of the vacuum state of interacting quantum fields

"Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is not bounded below for thermal ...
6
votes
1answer
368 views

Defining the ground state energy of a QFT

I would like to hear of some general discussion on how is the ground state and its energy defined in QFT and how does one go about finding it. (..at least in some simple cases I have seen the use of ...
12
votes
1answer
1k views

How to interpret vacuum instability of Higgs potential

If the Higgs mass is in a certain range, the quartic self-coupling of the Higgs field becomes negative after renormalization group flow to a high energy scale, signalling an instability of the vacuum ...
3
votes
2answers
791 views

Who first realized the uncertainty principle allows for virtual particle pair production?

For all I've read about Quantum Field Theory I've never seen the concept of the living vacuum accredited to someone in particular. Given the importance of this very application of the uncertainty ...
1
vote
0answers
271 views

Gravitation and the QFT vacuum

I'm asking this to get yet another lessson in the inability of QFT and GR to cohabit. Many people believe GR must yield to quantization. The question here is as to why the activity of the vacuum ...
12
votes
7answers
1k views

Can energy be taken out of the QFT vacuum?

There have been recent questions about the vacuum. In my simplified knowledge the vacuum is like a ground state energy level, and also that there might even exist other lower energy levels than the ...
3
votes
1answer
234 views

The vacuum as trigger

Do the apperance in the atomic nucleus of virtual matter-antimatter particle pairs play a role in the random nature of radioactive decay?
-1
votes
1answer
503 views

The difference between free energy and perpetual motion [closed]

What is the difference between free energy (over unity) and perpetual motion? Please provide some examples, both real world and theoretical.
6
votes
2answers
861 views

Wheeler-Feynman theory, QED without fields, vacuum polarization

Initially Wheeler and Feynman postulated that, the electromagnetic field is just a set of bookkeeping variables required in a Hamiltonian description. This is very neat because makes the point of ...