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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Mon, 16 Sep 2002 11:11:01 +0200

At 10:06 -0700 10/09/2002, George Levy wrote:

*>The impossibility of the Kirks to occupy the same position at the
*

*>same time during the transport experiment reminds me of fermionic
*

*>versus bosonic behavior.
*

Interesting. Shadows of a link fermion/boson and the 1-3 person

duality?

*>I wonder if there is a connection between fermions/bosons and the MWI.
*

Sure there is. Nice project to work on. And then it would be funny

to look at anyons too, in the MWI.

Fermion/bosons comes from symmetrical versus antisymmetrical behavior

after permutations. The "simple" proof that all quantum object are bosons

or fermions does not work for two dimensional spaces (three dimensional

space-time). In two dimensions you can have intermediate between bosons

and fermions, with intermediate crazy statistics. You can build

a fault tolerant quantum computer by doing knots with anyon's paths (cf Kitaev,

Freedman, etc.).

In some sense anyons remember the way they are permutated or substituted.

(If we were made of anyons the comp subst. level would be very low and

entangled with the ambient topology).

The big change with anyons is the generalization from the group of

permutations S_n (so important for fermions and bosons) to the group

of braids B_n (*).

Perhaps you were right, a long time ago, about intermediate

between 1 and 3 person. This would follow from your analogy 1/3 boson.fermion,

+ the existence of anyons.

A nice intro to braids and anyons is the John Baes

http://math.ucr.edu/home/baez/braids.html

Bruno

(*) Discovered by Emil Artin in 1920. It is a formidable mathematical

object. Patrick Dehornoy discovered some special order on B_n by

speculating on the existence of very high cardinals in set theory.

Later the same property have been proved without those high cardinals.

The group of braids gives also birth to the braided monoidal (tensorial)

categories I keep mentioning to Tim (cf the Yetter-post).

Received on Mon Sep 16 2002 - 02:15:36 PDT

Date: Mon, 16 Sep 2002 11:11:01 +0200

At 10:06 -0700 10/09/2002, George Levy wrote:

Interesting. Shadows of a link fermion/boson and the 1-3 person

duality?

Sure there is. Nice project to work on. And then it would be funny

to look at anyons too, in the MWI.

Fermion/bosons comes from symmetrical versus antisymmetrical behavior

after permutations. The "simple" proof that all quantum object are bosons

or fermions does not work for two dimensional spaces (three dimensional

space-time). In two dimensions you can have intermediate between bosons

and fermions, with intermediate crazy statistics. You can build

a fault tolerant quantum computer by doing knots with anyon's paths (cf Kitaev,

Freedman, etc.).

In some sense anyons remember the way they are permutated or substituted.

(If we were made of anyons the comp subst. level would be very low and

entangled with the ambient topology).

The big change with anyons is the generalization from the group of

permutations S_n (so important for fermions and bosons) to the group

of braids B_n (*).

Perhaps you were right, a long time ago, about intermediate

between 1 and 3 person. This would follow from your analogy 1/3 boson.fermion,

+ the existence of anyons.

A nice intro to braids and anyons is the John Baes

http://math.ucr.edu/home/baez/braids.html

Bruno

(*) Discovered by Emil Artin in 1920. It is a formidable mathematical

object. Patrick Dehornoy discovered some special order on B_n by

speculating on the existence of very high cardinals in set theory.

Later the same property have been proved without those high cardinals.

The group of braids gives also birth to the braided monoidal (tensorial)

categories I keep mentioning to Tim (cf the Yetter-post).

Received on Mon Sep 16 2002 - 02:15:36 PDT

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