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dpa
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Hi all,
what is the meaning/difference between perturbative and non perturbative vaccum.
what is the meaning/difference between perturbative and non perturbative vaccum.
Non-vanishing vacuum state
If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator (or more accurately, the ground state of a QM problem). In this case the vacuum expectation value (VEV) of any field operator vanishes. For quantum field theories in which perturbation theory breaks down at low energies (for example, Quantum chromodynamics or the BCS theory of superconductivity) field operators may have non-vanishing vacuum expectation values called condensates. In the Standard Model, the non-zero vacuum expectation value of the Higgs field, arising from spontaneous symmetry breaking, is the mechanism by which the other fields in the theory acquire mass.
...Vacuum energy is the zero-point energy of all the fields in space...the energy of the vacuum, which in quantum field theory is defined not as empty space but as the ground state of the fields...
The zero-point energy is ...the expectation value of the Hamiltonian; here, however, the phrase vacuum expectation value is more commonly used, and the energy is called the vacuum energy...
Yes, in a certain sense the perturbative vacuum is 'empty'; it's annihilated by typical field operators, so the result for counting particles in the vacuum is zero (after normal ordering); the examples you give (condensates like BCS, QCD ground state, non-vanishing vev for Higgs, ...) are all examples for non-perturbative vacuum states.Naty1 said:I'm not getting this yet...
"Typically a non-perturbative vacuum is not 'empty'...
is a perturbative vacuum 'empty'...? that doesn't sound like this description ??
...so the result for counting particles in the vacuum is zero
dpa said:hi,
could you give physical meaning rather than mathematical.
I am not an expert you see.
marcus said:Is the number of particles in a region always well-defined?
Say in the case the geometry is curved, or there are different observers?
I've heard people say it's not a well-defined concept.
marcus said:Is the number of particles in a region always well-defined?
Say in the case the geometry is curved, or there are different observers?
I've heard people say it's not a well-defined concept.
martinbn said:No, it is not well defined in curved beckground, in the sense that it is coordinate dependent. But i have also heard that even in flat spacetime (and only inertial systems considered) 'particle' is not well defined in a bounded region.
martinbn said:No, it is not well defined in curved beckground, in the sense that it is coordinate dependent. But i have also heard that even in flat spacetime (and only inertial systems considered) 'particle' is not well defined in a bounded region.
marcus said:I have seen what you heard demonstrated mathematically*. It seems that the idea of "particle" and the number of particles taking part in any given circumstance is highly observer dependent and geometry dependent.
"Particle" seems very far from being a fundamental, background independent, concept. More of a mathematical convenience useful in specific circumstances. Rather than something in nature.
Vacuum also observer dependent.
*Google "rovelli particle" and get http://arxiv.org/abs/gr-qc/0409054 What is a particle?
Is the number of particles in a region always well-defined?
Say in the case the geometry is curved, or there are different observers?
I've heard people say it's not a well-defined concept.
..uniquely-defined particle states do not exist in general, in QFT on a curved spacetime. ... in general, particle states are difficult to define in a background-independent quantum theory of gravity.
Perturbative vacuum states refer to the ground state of a quantum field theory in which interactions between particles are treated as small perturbations. Non-perturbative vacuum states, on the other hand, take into account strong interactions between particles and cannot be described using perturbation theory.
Perturbative and non-perturbative vacuum states are used in theoretical physics to understand the behavior of quantum systems and predict their properties. Perturbation theory is often used to approximate solutions to problems that cannot be solved exactly, while non-perturbative methods are necessary for systems with strong interactions.
No, non-perturbative vacuum states cannot be calculated exactly. This is because strong interactions between particles make it impossible to solve the equations that describe these systems analytically. Instead, numerical methods and approximations are used to study non-perturbative vacuum states.
Non-perturbative vacuum states are crucial in understanding the behavior of particles and their interactions at high energies. These states provide a more accurate description of quantum systems and are necessary for predicting the properties and behaviors of particles under extreme conditions.
No, perturbative and non-perturbative vacuum states are not mutually exclusive. In fact, perturbative states can be used as an approximation to non-perturbative states in certain situations. However, non-perturbative states are necessary for a complete understanding of quantum systems, especially those with strong interactions.