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Quantum Field Theoriesas

Statistical Field Theories

Antoine TilloyMax Planck Institute of Quantum Optics, Germany

Oberseminar Mathematische Physik LMU, Munich, GermanyFebruary 1, 2017

First problem:

Quantum field theory is not about fields, there are no fields, itsabout correlation functions of ... macroscopic stuff made of ...

(x1)(x2)(x3)(x4) =

(x1)(x2)(x3)(x4) =

what we want what we get

First problem:

Quantum field theory is not about fields, there are no fields, itsabout correlation functions of ... macroscopic stuff made of ...

(x1)(x2)(x3)(x4) =

(x1)(x2)(x3)(x4) =

what we want what we get

Second problem:

Even as operational theories, physical interacting quantum fieldtheories are ill defined.

(x1)(x2)(x3)(x4) =+k=0

()k gk

(x1)(x2)(x3)(x4) =+k=0

()k gk

These are actually the two classes of difficulties noted by Paul Dirac in 1963

Second problem:

Even as operational theories, physical interacting quantum fieldtheories are ill defined.

(x1)(x2)(x3)(x4) =+k=0

()k gk

(x1)(x2)(x3)(x4) =+k=0

()k gk

These are actually the two classes of difficulties noted by Paul Dirac in 1963

Reformulations of quantum theory are needed

The Bohmian way

dQk(t)dt = v

k (Q1(t), ,Qn(t))

i ddt = HL. de Broglie 1927

D. Bohm 1952

The Bohmian way

dQk(t)dt = v

k (Q1(t), ,Qn(t))

i ddt = HL. de Broglie 1927

D. Bohm 1952

Subtleties

Lorentz invariance

Either fixed foliation of foliation determined by the wave function the letter but not the spirit

Particle creation-annihilation 2 solutions

Stochastic creation-annihilation events Resurrect the Dirac sea

Subtleties

Lorentz invariance

Either fixed foliation of foliation determined by the wave function the letter but not the spirit

Particle creation-annihilation 2 solutions

Stochastic creation-annihilation events Resurrect the Dirac sea

Subtleties

Lorentz invariance

Either fixed foliation of foliation determined by the wave function the letter but not the spirit

Particle creation-annihilation

2 solutions

Stochastic creation-annihilation events Resurrect the Dirac sea

Subtleties

Lorentz invariance

Either fixed foliation of foliation determined by the wave function the letter but not the spirit

Particle creation-annihilation 2 solutions

Stochastic creation-annihilation events Resurrect the Dirac sea

The Collapse way

A modified Schrdinger equation

t |w = iH |w+ tiny(w, w)

A primitive ontology

fields, particles, flashes

The Collapse way

A modified Schrdinger equation

t |w = iH |w+ tiny(w, w)

A primitive ontology

fields, particles, flashes

What is known:

A Lorentz invariant GRW (Tumulka, 2006)

but no interactions and a wave function formalism

A Lorentz invariant CSL (Bedingham, 2011)

but a non-linearity in the smearing function making the statisticalinterpretation unclear

In both cases anyway, predictions = QFT.

What is known:

A Lorentz invariant GRW (Tumulka, 2006)

but no interactions and a wave function formalism

A Lorentz invariant CSL (Bedingham, 2011)

but a non-linearity in the smearing function making the statisticalinterpretation unclear

In both cases anyway, predictions = QFT.

What is known:

A Lorentz invariant GRW (Tumulka, 2006)

but no interactions and a wave function formalism

A Lorentz invariant CSL (Bedingham, 2011)

but a non-linearity in the smearing function making the statisticalinterpretation unclear

In both cases anyway, predictions = QFT.

What is known:

A Lorentz invariant GRW (Tumulka, 2006)

but no interactions and a wave function formalism

A Lorentz invariant CSL (Bedingham, 2011)

but a non-linearity in the smearing function making the statisticalinterpretation unclear

In both cases anyway, predictions = QFT.

Objective:

Construct a relativistic collapse model, naturally written as aLorentz invariant statistical field theory, that can be embeddedwithin an orthodox interacting quantum field theory.

In provocative form

1. Collapse models can be made equivalent to quantum theory2. Quantum field theories can be written as statistical field

theories3. The two previous points are equivalent

Objective:

Construct a relativistic collapse model, naturally written as aLorentz invariant statistical field theory, that can be embeddedwithin an orthodox interacting quantum field theory.

In provocative form

1. Collapse models can be made equivalent to quantum theory2. Quantum field theories can be written as statistical field

theories3. The two previous points are equivalent

Objective:

Construct a relativistic collapse model, naturally written as aLorentz invariant statistical field theory, that can be embeddedwithin an orthodox interacting quantum field theory.

In provocative form

1. Collapse models can be made equivalent to quantum theory

2. Quantum field theories can be written as statistical fieldtheories

3. The two previous points are equivalent

Objective:

In provocative form

1. Collapse models can be made equivalent to quantum theory2. Quantum field theories can be written as statistical field

theories

3. The two previous points are equivalent

Objective:

In provocative form

theories3. The two previous points are equivalent

dynamical reduction models

A modified Schrdinger equation

t |w = iH |w+ tiny(w, w)

A primitive ontology

fields, particles, flashes

an instantiation: the csl model

Linear collapse equation:

ddt |w(t) =

{iH0 +

R3

d3x M(x)wt(x)white

2 M2(x)

}|w(t) ,

with M(x) =1

(2)32

Nk=1

R3

dyk mk e |xyk|

2

22 |yk yk| ,

Master equation for t = E[|w(t) w(t)|

]ddt (t) = i [H0, (t)]

2

R3

d3x[M(x), [M(x), (t)]

].

More generally t = t 0with linear Completely Positive Trace Preserving

needs to be an unraveling of a nice open-system evolution

Gisin Diosi

an instantiation: the csl model

Linear collapse equation:

ddt |w(t) =

{iH0 +

R3

d3x M(x)wt(x)white

2 M2(x)

}|w(t) ,

with M(x) =1

(2)32

Nk=1

R3

dyk mk e |xyk|

2

22 |yk yk| ,

Master equation for t = E[|w(t) w(t)|

]ddt (t) = i [H0, (t)]

2

R3

d3x[M(x), [M(x), (t)]

].

More generally t = t 0with linear Completely Positive Trace Preserving

needs to be an unraveling of a nice open-system evolution

Gisin Diosi

an instantiation: the csl model

Linear collapse equation:

ddt |w(t) =

{iH0 +

R3

d3x M(x)wt(x)white

2 M2(x)

}|w(t) ,

with M(x) =1

(2)32

Nk=1

R3

dyk mk e |xyk|

2

22 |yk yk| ,

Master equation for t = E[|w(t) w(t)|

]ddt (t) = i [H0, (t)]

2

R3

d3x[M(x), [M(x), (t)]

].

More generally t = t 0with linear Completely Positive Trace Preserving

needs to be an unraveling of a nice open-system evolution

Gisin Diosi

an instantiation: the csl model

Linear collapse equation:

ddt |w(t) =

{iH0 +

R3

d3x M(x)wt(x)

2 M2(x)

}|w(t) ,

Normalization and cooking:

w(t) = |w(t)w(t)|w(t)dt(w) = w(t)|w(t) d0(w)

wt(x) = 2 M(x)+ bt(x)

white.

an instantiation: the csl model

Linear collapse equation:

ddt |w(t) =

{iH0 +

R3

d3x M(x)wt(x)

2 M2(x)

}|w(t) ,

Normalization and cooking:

w(t) = |w(t)w(t)|w(t)dt(w) = w(t)|w(t) d0(w)

wt(x) = 2 M(x)+ bt(x)

white.

an instantiation: the csl model

The good choice of primitive ontology is w, not M(x):

Is the natural object appearing in the linear eq. Does projects down to R3 the localization of the state:

wt(x) = 2 M(x)+ bt(x)

white

Allows to reconstruct the state exactly: w |w Allows a time symmetric formulation of collapse

Bedingham & Maroney (2015)

Is the natural Lorentz invariant object in generalizationsTumulka (2006), Bedingham (2011)

Allows quantum classical couplingAT & Disi (2016)

an instantiation: the csl model

The good choice of primitive ontology is w, not M(x):

Is the natural object appearing in the linear eq.

Does projects down to R3 the localization of the state:wt(x) = 2

M(x)+ bt(x)

white

Allows to reconstruct the state exactly: w |w Allows a time symmetric formulation of collapse

Bedingham & Maroney (2015)

Is the natural Lorentz invariant object in generalizationsTumulka (2006), Bedingham (2011)

Allows quantum classical couplingAT

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