The Sorrows of an American, by Siri Hustvedt

It is a rare writer who can both rouse the mind and grip the heart, and all the while provide the sensuous delights of image and language. In her new novel, as in What I Loved, Siri Hustvedt does that and more. The "more" is a compelling narrative in which the past haunts the present of characters so vividly real they become members of your intimate circle and erupt in your dreams.

Erik Davidsen – tall, thin, lugubrious, lonely, permeated by the voices of his patients – is a divorced New York shrink whose father has recently died, leaving behind a memoir of life in Depression-era rural Minnesota and war in the Pacific. The secrets of his father's life possess Erik, as well as the inevitably unfinished business between them. This is the very stuff of mourning.

Indeed, it is under the arc of mourning and melancholia that the action unfolds, bringing in its train the broader social mourning attendant on the tragedy of the Twin Towers. In this novel, the brain, as the great positivist Auguste Comte said, "is a device by which the dead act upon the living" – a process Erik documents in the journal through which he carries on a conversation with his father.

Erik's sister, Inge, equally lonely since the death of her husband, the iconic literary figure Max Blaustein, writes about philosophy. The dialogue between philosophy and psychoanalysis, as well as the relationship between brother and a sister who as a child was transfixed by "spells", is one of the many glories of this book. While Erik contends with patients, the past and a loveless present, Inge is enmeshed in a battle over potentially revealing letters with a woman discovered to be her husband's one-time mistress. A journalist pursues her, while her husband's biographer doubles as her lover, unable to distinguish the widow from his subject.

All this is unveiled slowly and counterpoints Erik's entanglement with his new neighbours – the beautiful Jamaican artist, Miranda, over whom he lusts, and her daughter Eglantine, or Eggy, who aptly calls Erik the worry doctor. Her own father seems to have vanished, only to re-emerge as a crazed stalker who is also a post-modern artist, a thief of appearances. Out of hundreds of snapshots, he reconstructs a reality which nudges Erik into a recognition of his own violence.

This gives little sense of this novel's bracing subtlety, a texture in which dream, memory, intimacy and the streets mingle to create a thick semblance of lived life. Few fictional shrink, and perhaps fewer real ones, have had Hustvedt's gift for translating the essence of an analytic session or the slippery pared-down imagery of dream into prose. Eggy's chats with Erik, the way he allows her to tie him and the furniture up when she's attempting to link the various fragments of her life together, are both model and intensely moving encounters.

So, too, are Erik's attempts to deal with the sufferings of his patients. These are only sometimes successful, but always revealing. The narratives of Ms L who feels "frozen out" and in her rage creates an abuse story of the past for herself, or Mr T with his "death-tattlers", racing puns and rhymes, punctuate and puncture a world in which – as Eric's one-time supervising analyst underlines – "wholeness and integration" are necessary myths. Closer to the truth is the fact that we are all "fragmented beings who cement ourselves together, but there are always cracks". Erik, Miranda, Inge, even her adolescent daughter – who carries the double freight of having witnessed the falling figures on 9/11 – all learn to live with the cracks while they frequent their ghosts. The wonder is that, out of this brew of death and depression, Hustvedt somehow creates an exhilarating fiction. The clue may lie in her finely calibrated understanding of the many manifestations of love.

If the novel has any weaknesses, these are intriguingly to do with the secrets of the all-American, and hence immigrant, parental past. But uncovering these, however minimal, is part of the work of "turning ghosts into ancestors", which is what Hustvedt herself has done.

The parental death in the novel is that of her own father, who died in 2003 and whose memoir is cited here and there through its mesmerising pages. This is a book that's almost impossible to put down, and even harder not to re-read.

Lisa Appignanesi's 'Mad, Bad and Sad: a history of women and the mind doctors' is published by Virago