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Perturbative and non perturbative vaccum states. 
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#1
Mar1312, 12:12 AM

P: 149

Hi all,
what is the meaning/difference between perturbative and non perturbative vaccum. 


#2
Mar1312, 05:23 PM

Sci Advisor
P: 5,451

Let's start with a simple explanation:
The perturbative or Fock vacuum 0> is simple described by a_{n}0> = 0 for all possible quantum numbers n. The nonperturbative ground state is describe by something like (HE°)Ω> = 0 with minimum E°. Alternatively one could write something like <0H0> ≥ <ΩHΩ> 


#3
Mar1412, 08:15 AM

P: 149

hi,
could you give physical meaning rather than mathematical. I am not an expert you see. 


#4
Mar1412, 10:50 AM

P: 7

Perturbative and non perturbative vaccum states.
A non perturbative vacuum may be topologically different from the trivial or ordinary vacuum. That is, one cannot use a topologically trivial transformation(homotopic to identical mapping) to transform it to the trivial vacuum. You can read some references on instanton to get more information.



#5
Mar1412, 05:14 PM

Sci Advisor
P: 5,451

Typically a nonperturbative vacuum is not 'empty'. In QCD you have chiral symmetry breaking with a nonvanishing order parameter indicating a phase transition. The order parameter is the socalled quark condensate [itex]\langle \bar{q}q\rangle \neq 0[/itex]. That means that in the phase where chiral symmetry is broken the 'vacuum' is not 'empty' but 'contains quarkantiquark pairs'.
Usually you would assume that [itex]\langle \bar{q}q\rangle = 0[/itex] b/c of normal ordering, but this applies only to the trivial vacuum state. 


#6
Mar1812, 10:20 AM

P: 5,632

Hi dpa:
I'm not getting this yet...... "Typically a nonperturbative vacuum is not 'empty'.... is a perturbative vacuum 'empty'.....???? that doesn't sound like this description:... [...the article provides some interesting background] and this: but I'm still not clear about the answer to your question.... 


#7
Mar1812, 10:39 AM

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P: 5,451




#8
Mar1812, 11:59 AM

P: 5,632




#9
Mar1812, 12:53 PM

Sci Advisor
P: 5,451

yes!



#10
Mar1812, 01:34 PM

Astronomy
Sci Advisor
PF Gold
P: 23,232

Is the number of particles in a region always welldefined?
Say in the case the geometry is curved, or there are different observers? I've heard people say it's not a welldefined concept. 


#11
Mar1812, 02:15 PM

Sci Advisor
P: 8,655

If the system is strongly interacting, then we may not know how to solve our equations to get the true ground state. If there is a noninteracting system whose ground state we do know, then we may try to write the true ground state approximately as the ground state of the noninteracting system plus some, hopefully small, corrections. (That doesn't always work.) 


#12
Mar1912, 08:47 AM

P: 354




#13
Mar1912, 01:07 PM

Astronomy
Sci Advisor
PF Gold
P: 23,232

"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/grqc/0409054 What is a particle? 


#14
Mar1912, 01:15 PM

P: 97

The particle number operators in 2 bounded disjoint region do not commute for spacelike separations (i's not a local function of the fields), they only approximately commute for high separations. What is an observable is for example the charge contained in any bounded region. Ilm 


#15
Mar1912, 01:52 PM

P: 354




#16
Mar1912, 04:14 PM

P: 5,632

Starting with just
I'd be really doubtful on a conceptual basis that a particle would be well defined if we know all our best theories falter at the singularity of a black hole....are there even 'particles' [mass, space] in those extreme conditions......where do they 'go' ....in fact where does space go....that seems a 'singularity' in time....it only takes a single exception like this to hint the rest of GR and QM are most likely approximations....it's perhaps not just particles that may not be so well defined as we take them to be in everyday less extreme conditions. String theory suggests that it may be the configuration of higher dimensional spaces that influences string [particles] properties....their vibrational patterns and energies for example ....so when spacetime jiggles around or morphs from one region to another it seems plausible that our perception of particles might also change...because they change. Further, the Unruh effect [regarding vacuum state temperatures] suggests different observers read coincident spacetime vacuum conditions differently....another hint that things globally and locally may be more surprising then we expect. Both these concepts seem to support Marcus post. I read Rovelli's Introduction and this caught my attention: I put the article on my reading list.... 


#17
Mar2012, 09:51 AM

P: 5,632

For those who might be interested in a complementary discussion, with some good explanations of the mathematical apparatus involved, check this one from March 2010:
What is a Particle. http://www.physicsforums.com/showthread.php?t=386051 More on Fock states, operators,Poincaire Group, local versus global representations, etc,etc..it's a long one. After I started reading 'What is a Particle' this time around I thought 'This sounds familiar' whereupon my enfeebled memory kicked in and I found Marcus had previously baited me on the same topic [!!!] instigating the 2010 discussion. [Note: I still don't understand the rules here on posting in old threads, but I recently got 'censored' by a moderator when I inadvertently posted an old one....so be warned!] 


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